There are a few things you need to watch out for when getting custom models.
After you subscribe to something, go to
Documents\ManiaPlanet\Skins\Models\StadiumCar. Create the
StadiumCar folder inside
Models if you don't see it already. This is where you should be placing downloaded car models' .zip and .loc files. Both of these are needed for it to work correctly. After this, restart the game so it can find the new files.
If your router ports don't forward automatically, you'll need to open
2350 UDP & TCP and
3450 UDP & TCP. This is required for the game to use your model's .loc file to get it from the internet for other players to see.