They semi explained this Kyler went through a series of tests. They taped the ankle, couldn't push off it, back again they took an xray apparently, they then re taped the ankle. He said he was waiting on things to kick in and loosen up which makes it pretty likely they put him on something for the pain and were waiting, either for him to get it numb enough to play, or for him to come down enough off the initial painkiller whatever it was to function. When I blew out my knee and they gave me a shot to allow them to straighten the leg out didn't feel a thing, and I couldn't have played sandlot football let alone NFL I couldn't function at all due to the shot. I have no idea what Kyler got it it's entirely possible it took time to get him back to ok he's not in pain AND he can think and function.
I would add they were also probably waiting to see how the game went, if they fell way behind no point putting him in, if it stays relatively close maybe he can come back and win the game. One drive earlier would have been nice but we have no idea clearly Kliff didn't know he was ready to go so it's not like they were asking him to play and he said no, they didn't think he could