Don't recall ever seeing anyone throw 15 pitches between innings, unless the ump was stuck in the bathroom. The most common complaint is that umps will not allow the customary number, which is around 8.
But, assuming the ump is not an issue, it is really up to the player and how he feels. Sometimes during HS/Legion ball my son would only throw 2 or 3 and tell the catcher to throw down to 2d. I asked him about it once and his response was "I'm already loose, and I need to go deep in the game. I'm just trying to save my bullets."
As far as pitch counts are concerned, I believe the counts recommended by ASMI assume a reasonable number of warm up throws between innings. BUt if the player is throwing an excessive number you may want to count them. Ditto if he's making an excessive number of full speed picks to first.