That's where it could get tricky, since the game really doesn't know that you are multi-class racing. It just knows the bloke with the BF1 has the fastest lap.
I think there should be an option where if you pull into the garage forwards, it spectates you, and if you back in, it puts you in the pits. It would add a nice little touch of realism, and could be turned off and on if someone doesn't want it.