I believe when you are instantiating the button to have an action, like when you say button.setOnAction(evt -> method());, you can have it call multiple methods at the same time.
You can do button.setOnAction(evt -> {method1(); method2()});
Another way of doing this is just having the button call one method, but that method calls two separate methods for the actions that you want it to do.
If you want a separate method to be called for when you press it vs when you release it, you just have to set those up separately using onMousePressed() and onMouseReleased()