Upper pulley too close to chain
This sort of rub occurring in small/small, or the smallest cog of a 1x, is a symptom of the chain being too long, either because it was installed without being sized properly, or because it was a compromise made to cheat the maximum capacity of a rear derailleur, or because a cassette was swapped in that required less chain wrap and it effectively became too long, or because the bicycle has horizontal dropouts and the wheel has been moved forward from the position where the derailleur was able to tension the properly. 

If your trainer has a cassette installed with a smaller smallest cog than what your chain was sized for, that would cause this. (A lot of mechanics size road chains based on preventing droop in small-small because this actually gives maximum cassette swappability for wheel changes.)

Because the bike has horizontal dropouts, it could also be happening in whole or part if the chain was sized for a wheel orientation that was further back, whereas in the picture you have it slammed.