First, after every play a cursory look at that play is performed. If, after that first look, the replay official decided that a formal look is in order he will notify the Referee who will stop the game and notify all involved that the prior play is under review. In this play it did not happen because after that cursory look, it was determined that the call was correct.
They know the play wasn't being reviewed because the Referee did not declare an Official's Time Out. This wasn't breaking news for the coach, or for any coach for that matter as they were told prior to the game how the process works. The basic premise for replay is that the ruling on the field is correct. The coaches are to assume that the play has been ruled correctly until the Referee stops the game to conduct the review.
As far as time outs are concerned. It seems he choose to run the clock down in hopes that the guys in the booth would intervene. If so, he chose poorly.
There were many in attendance (on both sides) that questioned how the other 5 time outs allotted to him were managed as well.
Agree with you here except for one point.... The officials on field have nothing to do with the process.
Remember, the coaches wanted this.