How to trigger exit animations on button press

The title doesn't fully capture the question though. I can use pause timeline to hold an exit animation until a button is pressed but what I'm struggling with is when I want to also have that button press also jump to a new layer (or slide) while having the exit animations trigger before the layer/slide change. I can't seem to reliably have my cake and eat it too.

For clarity, what I'm trying to achieve (in as simple a manner as possible) is to have an image on screen with a "Continue" button or hotspot on it that, when clicked, will show a new layer with a new image (I'm using this method to create interactivity when learning a new software program so learners can actually click through the process). I also want to have the image (and button) fade or zoom out to reveal what is on the next layer to create a visual cue that, for example, a pop up window has closed to return the user to the previous screen that was behind it.

I've been muddling my way through this and have created a couple instances that have worked but it feels very clumsy. Is there a simple way to achieve this?