It will fire on release if set up to do that
It can also be set up to fire after a set amount of time.
I get the delayed switching when using the standard TAP way to switch. Like if I play a continous rhythm without changing the chord and I click the FS12 ON the beat, the first note will start out with the previous sound for a short but very noticeable while before switching to the new sound. And I can't blame it. It has no idea which scene I'm going to choose.
My suggestion is an attempt to prepare the AXE for which scene to go to, because as soon as I hold the button down, it knows what will happen next. It's no problem for me to hold the button down for a second or two before releasing it, if that is what it takes.