The pieces will only shift if they are "settled", meaning they have fallen through the board as far as they can. We didn't want the game to work like tetris where you can have theoretically complete control over where the pieces land, so this is what we ended up with.
There are some interesting effects in the game as a consequence of this! Try moving a stack of pieces all the way to the edge of the board, squishing the stack against a falling token
Thanks for playing!