The starter solenoid 3/8" stud post is used as a junction terminal for battery voltage distribution (12v) throughout the engine and controls. Yes the reds are right.
The yellow wire or red wire with a yellow stripe is 12v from the remote control when the ignition key is in the START position. It applies 12v to an electrical coil inside the solenoid via one of the small terminals, not the large terminal as you mentioned, and if the coil is not internally grounded to the engine block through the mounting of the solenoid, there is a second small terminal that has a black wire attached which routes to the engine block to provide battery - (ground) and complete the circuit.
So yes, the yellow is on the wrong terminal. What's confusing to me here and you there, is that the current terminal is 3/8" and the correct one is like 1/8". If the lug is still attached, it is grossly out of proportion unless PO cut it off and either attached a different terminal sized to suit or just wrapped the bare wire around the stud.
The kill switch in the control box is ground when in the off position and is the black/yellow stripe (or yellow with black stripe...one is kill the other fuel enrichment and always forget which is which) and takes that ground to the trigger circuits and grounds them killing the engine.
So sir, move the yellow wire and your starter should work for you with the key.
Mark
Thanks.