Totally right. You didn't have to run all the 93 out before you started the 87. The failsafe is just for that to keep damage from happening.Not a problem running 93 octane on a 87 octane tune. You just don't want it the other way around: don't run anything less than 93 octane on the 93 octane tune.
I'm guessing your PCM detected a too lean condition and went into limp home mode to protect your engine from damage.