I've read about unstarts before and never got the impression that the engine in question stopped. It was the shockwave configuration at the inlet that had to be "restarted"?
Yes I believe that is correct but one consequence of an intake unstart in a J58 is that the afterburner will also stop functioning. I'm not sure what the proper term is when an afterburner stops producing thrust. Maybe flame out?
Regardless, this was the cause of the violent yaw/roll action associated with an unstart (loss of thrust). When the intake was reconfigured the afterburner had to be re-lit and in a J58 this requires TEB. So while TEB was not used to correct the unstart it still had to be used after an unstart.