Fuse 10 supplies TSM and switch connector (on pre 2014 models) and is itself fed by ignition switch. Hazard lights are fed by permanently live fuse 2 so not too surprised at your findings as some back feeding taking place.
Note the TSM appears to be different on later post mid 2014 models as the connector is an 18 pin one (16 used) whereas earlier type which I believe you have, uses a 12 pins. Note also earlier models had isolation diodes added externally to left and right indicator circuits at switch connector probably to avoid hazard wiring causing cross feed. Might be worth checking these although probably covered with heat shrink.
TSM's seem to have random built in issues from new even the later ones but I would be tempted to increase fuse 10 size from 5 to 7.5 or even 10 amps and see if that cures blowing issue.
