Judging by your demo, I asume you're making a platform game. If this really is the case, then I'm uncertain as to why you want to have your sprites aligned with the tiles every time they are moving.
It is in any case not what normally happens in platform games, and might be confusing to the player or perhaps even annoying, because the sprite will continue to move until it is aligned with a tile. Even when the user has stopped pressing the buttons.

I could be wrong here, but i think you need to look for a different solution.