What you describe is normal. When you buy ultimate edition, or any DLC, the cars don’t automatically show up in your My Cars list (your game garage). However, those cars are available for you to add to your garage through the autoshow for zero credits. If you didn’t have Ultimate Edition, you’d be prompted to purchase those cars or car packs from the xbox store if you tried to buy them from the Autoshow in game.
Since you bought Ultimate Edition, you are entitled to add to your garage from the Autoshow for zero in-game credits all five cars from the VIP car pack, as well as the 30 cars which came in the first six monthly car packs. You own all these cars, but you still need to add them to your in-game garage if you want to drive them, customize them, etc:
VIP CARS
2013 Donkervoort D8 GTO
1967 Ferrari 330 P4
2014 Lamborghini Urus
1949 Mercury Coupe
2014 Tesla Model S
OCTOBER – MOBILE 1 CAR PACK
2015 Jaguar F-Type R Coupé
2014 Jeep Grand Cherokee SRT
1957 Maserati 300 S
2013 Renault Clio RS 200
1988 Volkswagen Scirocco 16V
NOVEMBER – FALKEN TIRE CAR PACK
2014 Alfa Romeo 4C
2014 BMW M4 Coupe
2014 Chevrolet Super Sport
1988 Lamborghini Jalpa
1969 Toyota 2000GT
DECEMBER – NAPA CHASSIS® CAR PACK
2015 McLaren 650S Coupe
1970 Buick GSX
1988 Chevrolet Monte Carlo Super Sport
2014 Land Rover Range Rover Supercharged
2015 Audi RS 6 Avant
JANUARY – G-SHOCK CAR PACK
2015 Nissan IDx NISMO
1953 Ferrari 500 Mondial
1975 Ford Bronco
2013 Shelby Ford F-150 SVT Raptor
1978 Subaru BRAT DL
FEBRUARY – TOP GEAR CAR PACK
2015 Lexus RC F
2015 BMW M235i
2015 Ferrari 458 Speciale
1993 Jaguar XJ220
1986 Lamborghini LM002
MARCH – ROCKSTAR CAR PACK
2015 Volkswagen GRC Beetle
2015 Jaguar XFR-S
2015 Subaru WRX STI
1970 Volkswagen #1107 Desert Dingo Racing Stock Bug
1995 BMW 850CSi
There was also a free bonus car released along with every monthly pack, which all players can add to their garages at no cost.
You can also refer to this handy list by ManteoMax:
http://forums.forza.net/turn10_postst21959_Forza-Horizon-2---DLC-and-Editions-List.aspx