I had the same problem. In my case it was some trailer mod from Steam Workshop. Everytime the game wanted to use the trailer the game crashed. So I kicked it from my collection and now everything is fine.
The trainer works as perfect as usual Only strange thing I noticed: When I close the game with activated trainer then my truck has 100% damage after next game start. No problem when using the trainer to fix the truck, but strange anyways
I believe it works the same as in Euro Truck Sim 2:
Open your progress screen first, press Numpad 4, leave screen, return to the progress screen and the EXP should have changed.