This argument has gone on throughout the Megaman series. Super Adventure Rockman for instance showed Megaman doing a shotgun style lock and load to form his buster, but most cases either would cut away and have his buster suddenly appear or it would appear in a flash of light such as in day of Sigma. Let's just ignore that abomination Ruby Spears cartoon no matter how much some fans want to cling to it.
The Flash of light and cutaway methods seem to be most common. In either case we can probably assume that whatever transformation goes on, be it mechanical, nanomechanical, or even some kind of energy conversion, that the flash or cutaway is intended to show that it occurs too quickly to see with the naked eye.
If you want to work in the SAR and X3 intro versions we could assume that these are ultra slow mo shots to show you what is physically happening. At least in those revisions of the buster, as X would certainly have different transformations for different armors and later X busters and classic Megaman has had his buster upgraded at least twice since then.
I'll stick to "Too fast to see" explanation myself, as it fits with the gameplay with having almost no delay between normal hand at the side, and firing buster with the press of a button.