The fact the clock stopped initially because of a first down is the only thing that DOES matter.
here is a PDF listing helmet infraction procedures. Section 15 deals with the scenerio we are discussing.
https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.oficiales.org/1_reglas_NCAA/2015_Reglas/Originales/10-SECOND%20RUNOFF.pdf&ved=0ahUKEwjOj6m0go7WAhWRwYMKHYTvCEoQFggmMAE&usg=AFQjCNE0d495GmF6oo73Rz2kB6Sz-wMKrg
But to make the rule as simple as possible to understand.
If a foul, helmet removal, or injury in the final minute of a half stops the clock, there's a 10-second runoff option for the opponent. Otherwise, there is no option.
None of those three things stopped the clock. The first down did.
I read the scenario you mentioned, and it certainly sounds like you are correct. This, however, makes zero sense based on how the rule is written, and even just sheer common sense. A first down is a TEMPORARY stoppage of the clock, only long enough to spot the ball and move the chains; so I am baffled as to why it should prevent a 10-second runoff.
However, even taking this into account, the refs STILL blew the play. Even disregarding any sort of 10-second runoff or Unsportsmanlike Conduct penalty (which should have been called), they still handled it wrong, and the Section 15 scenario even bears this out. Disregarding any of the other stuff, the player who lost his helmet should have been removed from the game, and then the ref should have signaled for the clock to start. Says it right there "Game clock start's on referee's signal"; you can also find it under Rule 3-3-2-e which says
"Starts on the Referee’s Signal. For each of the following reasons, the game clock is stopped on an official’s signal. If the next play begins with a snap, the game clock will start on the referee’s signal: 16. A player’s helmet comes completely off through play".
If they had handled it correctly, the ref should have blown his whistle, told the player to leave the field (who was already leaving the field as it was, so I'm not sure why every single one of them felt the need to start tweeting away with their whistles) and once he started to leave the field, signaled for the clock to start again. Instead, they blew their whistles, stood around for a while, and then let ASU easily kick a field goal, starting the clock on the snap rather than the officials signal. They blew it, plain and simple.