I have a late 2006 FXSTC and when it is hot ,as in just ridden, and I turn it off, it spits back a couple of times on start up before it actually starts. It is getting worse and never does it cold. Can ride all day , no problem, but restart after stopping for fuel and it spits back real nasty. Certainly gets everyones attention at the servo.
Lozz my Street Glide did a similar thing and after doing the Compensator it stopped. There was more of a clunk when it turned over from start. A screaming budgie replacement did fix it but now needs a 3rd replacement after 80k in total from new. Good luck with it all
Sometimes tunes can drift over time if something changes and the system self learns to a degree, flash your tuned cal back in, it will clear fuel trims etc, see if it makes any difference.
Bike has been in bits for weeks now, awaiting parts. Screaming Eagle compensator & new rotor . Harley are so slow with parts, so I have nothing to tell you re it fixing dodgy start ups yet. Lucky I have another bike to ride but am missing the Harley.