When Mattel decided to phase-out any differences between the "Corgi Juniors" and "Hot Wheels" lines with a new line called "Corgi Auto-City," a new design was needed for the blisterpacks and any boxed items. The following picture shows the resulting packing style which was used from 1991 until sometime in 1994 (though some references state 1993 or 1995).
After Corgi did its buy-back and the two companies went their separate ways, the settlement 'gave' Mattel the "Auto-City" name and logo along with most, if not all, of the molds that had been used in Corgi's "Auto-City" line.It's not clear if Mattel used the molds (with the exception of the Skip Dumper mentioned on the Home page) or had a surplus stock of Corgi-labeled diecast that it needed to do something with. If the latter, I'm guessing that Mattel had two options: either junk the surplus and lose money or package the items and possibly make money.
Regardless of whether they used the molds and/or had surplus, it's obvious that Mattel decided to try and make money with what they had.
Their only 'real' cost would be in creating a new packaging design.
The result, pictured below, is usually referred to as the "transitional" design which was only used in 1996 (possibly as early as late 1995; and some references state 1994 through 1996 possibly because most of this style of packaging has a 1994 copyright).
It's called "transitional" because one of the things Mattel immediately did was to issue mainline Hot Wheels tampo-d with the "Auto-City" logo in regular Hot Wheels packaging. All of these vehicles were original Hot Wheels, the adapted Corgi molds hadn't made any appearances just yet. {I'll come back to this shortly.}The separation of Corgi and Mattel happened at a time that Mattel was busy enlarging the Hot Wheels line in three other ways. First, 1994 saw the planning for the 1995 release of the new "Treasure Hunt" line. Second, 1994 also saw the planning for the 1995 release of the new "1995 Model Series" which eventually became the "First Editon" line. Third, 1994 also saw the planning for the release of the new 4-car 'Monthly' series.
With all this going on, it seems that Mattel didn't want to spend too much time/effort on incorporating its gains from Corgi into the regular Hot Wheels line. Apparently, it was easier to redesign the packaging (and the tampos for some vehicles) than to re-work all the molds 'into' "Hot Wheels" labeled molds.
As mentioned on the Home page, Mattel apparently knew that the buy-back was going to go through. And though busy with three new Hot Wheels lines, Mattel found time in 1995 to plan for, and take care of, the incorporation of the Corgi models into the regular Hot Wheels line.
The easiest to do was an "Auto-City" tampo design and one of the first items with this 'new' design was the 1996 "Auto-City" 5-pack. This pack contained the Fire Eater, Mazda MX-5 Miata, Peterbilt Dump Truck, Rig Wrecker, and a police car (either the Sheriff Patrol or the 'Holden Commodore' Police Cruiser). The Rig Wrecker and Police Cruiser were also released singly on blisterpacks with "Auto-City" tampos.

The Rig Wrecker was also blisterpacked with a flatbed semi in the "Long Haulers" line.

Once all the chassis had been changed to reflect "Hot Wheels", Mattel seemed to go gung-ho in using the vehicles.
One of the first items released was the 1996 "FAO Schwarz Gold Series III".

This set contained the '57 T-Bird Convertible, '80s Corvette, BMW 850i, BMW M3, Ferrari 308, Ferrari 348, Ferrari Testarossa, Ford Mustang Cobra, Ford Sierra, London Double Deck Bus, London Taxi, Mercedes 500SL, Mercedes-Benz 190E, Porsche 911 Targa, Porsche 935, and the Porsche Carrera -- all former Corgi models.
1996 also saw 12 former Corgi models (London Taxi, BMW 850i, Corvette Coupe, Ferrari 308 GTS, Ferrari 348tb, Ferrari Testarossa, Ford Mustang Cobra, Ford Sierra 2.3 Ghia XR4ti, Ford Thunderbird Convertible, Mercedes 500SL {single body casting}, Porsche 935, Porsche Carrera) released as Hot Wheels mainline vehicles. These 12 couldn't be released as "First Editions" since they had already appeared in the "Auto-City" line.Towards the end of Mattel's ownership of Corgi, a line with the "Hot Wheels Auto-City" banner called "Action Squad" appeared (the packaging is copyrighted 1995). Most of these were blisterpacks featuring one vehicle, a fold-up-into-a-box playset, and miscellaneous accessories. The entire packaging and design appears to be a predecessor to the once popular Hot Wheels "Action Pack" line that ran from 1997 till 2000. In fact, many Corgi models (with Hot Wheels bases/chassis) were introduced into the regular Hot Wheels line through the "Action Pack"s. The 'Surf Patrol' pack introduced the Off Road Racer and Dinghy with trailer. The 'Firefighting' pack introduced the Fire-Eater II and Flame Stopper II. The 'Construction' pack introduced the Digger (aka Dirt Rover & Excavator {not the "First Edition" one}) and Cement Mixer. All six of these appeared in 1997. As a side note, even most of the figures and accessories included in the "Action Pack"s were originally Corgi molds.
Others that appeared in 1997, in either "Action Pack"s or as a mainline, include the BMW M3, City Police, Porsche 911 Targa, Road Roller, Highway Builder, Sandstinger, and another Cement Mixer.
1998 seems to be the last year that any former Corgi models were introduced. The BMW 325i and Tipper were released on blisterpacks as mainline vehicles.
As of this writing, at least 36 Corgi models/vehicles have been introduced into the regular Hot Wheels line since 1996.
Though none of the original Corgi Haulers have as yet to appear in any Hot Wheels line, I wouldn't be surprised to find out that the Corgi Haulers inspired the Hot Wheels "Haulers" line -- especially knowing that the first group of Hot Wheels "Haulers" appeared in 1996 (very shortly after Corgi's buy-back).
Somewhat surprising is that the Hot Wheels "Auto-City" Haulers (using the Corgi molds) tend to be more in demand that the regular vehicles and fetch premium prices.
Also not used as of yet are the the Corgi Superhaulers. At this time, none are known to have been released in the Hot Wheels "Auto-City" line (or if Mattel even got those molds). But, again, I wouldn't be surprised to discover that the Corgi Superhaulers inspired the Hot Wheels lines of "Long Haulers" (aka "Pavement Pounders") and NASCAR "Transporter"s.
And there you have it -- the "Auto-City" impact on Hot Wheels!
NOTE: Unless packaged, it is completely impossible to determine which line (Corgi or Hot Wheels) a loose vehicle is from.
Which Corgi's became which Hot Wheels?The following is a list of all the known Corgi molds/vehicles/castings that have been incorporated and released as Hot Wheels "mainline" vehicles.
NOTE: Year in parentheses is original release date for that vehicle from its particular manufacturer.
Corgi --- Hot Wheels
Austin London Taxi (1980) --- London Taxi (1996)
BMW 325i (1988) --- BMW 325i (1998)
BMW 850i (1991) --- BMW 850i (1996)
BMW M3 racer (1988) --- BMW M3 racer (1997)
Buick Police (1976) --- City Police (1997)
Cement Mixer (1985) --- Cement Mixer (1997)
Chevrolet Corvette (1983) --- Corvette Coupe (1996)
Dinghy with trailer (1975) --- Dinghy with trailer (1997 - Action Pack only)
ERF Fire Engine (1975) --- Fire-Eater II (1997)
ERF Simon Snorkel Fire Engine (1972) --- Flame Stopper II (1997)
Excavator (1977) --- Digger / Dirt Rover / Excavator {not the FE} (1997)
Ferrari 308 GTS (1982) --- Ferrari 308 GTS (1996)
Ferrari 348tb (1991) --- Ferrari 348tb (1996)
Ferrari Testarossa (1988) --- Ferrari Testarossa (1996)
Ford Mustang Cobra (1981) --- Ford Mustang Cobra (1996)
Ford Sierra 2.3 Ghia (1983) --- Ford Sierra 2.3 Ghia XR4ti (1996)
Ford Thunderbird Roadster (1959) --- Ford Thunderbird Convertible (1996)
Ford Transit Wrecker (1981) --- Ford Transit Wrecker (1997)
Hot Rod Custom Van (1994) --- Custom Van (1998)
Iveco Tanker Truck (1988) --- Oil Refinery Truck (1998)
Jaguar XJ40 (1991) --- Jaguar XJ40 (1997)
Jaguar XJR9 (1991) --- Jaguar XJR9 or XJR12 (1997)
Jeep Rescue (1984) --- Off Road Racer (1997)
Land Rover (1988/1994) --- Land Rover MK II {slightly re-tooled} (1997)
London Bus (1982) --- London Bus (1996)
Mercedes 2.3 Taxi (1988) --- Mercedes 2.3 190E (1997)
Mercedes 300 TD station wagon (1994?) --- Mercedes 300 TD station wagon (1997)
{possibly "Fire Chief" station wagon found only in sets}
Mercedes 500SL (1982) {single body} --- Mercedes 500SL (1996) {single body}
Mobile Cement Mixer (1976) --- Cement Mixer (1997)
Porsche 911 Targa (1988) --- Porsche 911 Targa (1997)
Porsche "935" (1988) --- Porsche 935 (1996)
Porsche Carrera (1974) --- Porsche Carrera (1996)
Raygo Rascal 600 Road Roller (1970) --- Road Roller (1997)
Shovel Loader (1975) --- Highway Builder (1997)
Skip Dumper (1974) --- Sandstinger (1997)
Tipping Lorry (1977) --- Tipper (1998)