Is there a way to disable buttons while a tween is moving, so the user can't hit the button several times and allow for several instances of the tween running at the same time?
Just some code to go with this:
var tween = this.add.tween(object).to({x:0},duration,Easing,autostart,delay);
tween.onStart.add(function() { button.inputEnabled = false; }, context);
tween.onComplete.add(function() { button.inputEnabled = true; }, context);
And take a look at disabling buttons here : Phaser Examples - Disable button