1982 xj750 seca coughs only when I hit the off switch

So this is a really weird issue for yall. I got this bike about a year and a half ago and have been working on her off and on through that time. I’ve just recently fully rebuilt all the carbs and followed the church of clean and fully cleaned every little nook, cranny, and passage on these god forsaken carbs. Today I went ahead and put them back on the back and slapped the gas tank on top with some fresh gas. Gave her a bunch of cranks and got nothing. Fair enough I probably messed something up in the carbs and I hit the off button. And the weirdest thing right as I did that she coughed and turned over a bit. Did some more experimentation and the same thing if I turned her over and hit the stop button she’d cough and I could smell exhaust. And also weird only the 1st exhaust tube was warm to the touch. Now I believe the others aren’t coughing because I’ve got their pilot air/fuel mixture out of wack which I’m also super confused on adjusting. Anyways all I’m asking is why would it cough only when I hit the stop button? And how does one adjust their pilot air/fuel mixture screws properly?
Thank you all for your time

 

An equally weird answer is the possibility that the coils are not actually firing from a signal received from the pickup coils but instead from electrical anomalies OR the coils are firing with the wrong pulse. Remember these are a wasted spark ignition firing coils in a A-B-A-B-A-B-A-B to make up the 1A-2B-4A-3B firing sequence of the 1-2-4-3 firing order so maybe go back and check which pickup is firing which coil.
What I would do is pull all the plugs and let them rest against the cam cover then crank the engine and note if they're all firing in a rhythm. If you have an old-school timing light clip it to the #1 plug and with the left side engine cover off crank the engine and flash the timing pointer, #1 should flash pointer up.

So when the stop button is hit with the engine stopped the TCI may be firing an ignition coil which in turn fires some air/fuel and if an exhaust valve is open will pop off any raw air/fuel in the exhaust, this points to the firing sequence being reversed.

So assuming you're working with the HSC32 carbs with the fine thread pilot screws I always start out at 2-1/2 turns out from the stop point and work from there.