Add time delay before layer is visible

In Storyline, you can trigger something to happen when an animation completes.

If the "slide in and slide out" don't take too long, you could do this for each button that opens a layer: 

• Insert a shape off the slide. (For naming, I suggest something like Timer1, Timer2, and Timer3.)
• Add a motion path to the shape with a duration that matches how long the "slide out" takes. 
• On the button, use a trigger that moves the corresponding Timer object on its motion path when the button is clicked. 
• Have the "show layer" trigger run when the Time object's motion path completes. 

The caveat for this method: There would be a delay when the user first clicks a button (that is, when no layer is showing yet). If it takes too long, that could be frustrating for the user. A workaround would be to have a trigger that shows the layer when the button is clicked with a condition so it only happens if no layer is showing yet. "No layer is showing" isn't an option for a condition, but you could use a T/F variable to track whether any of the buttons have been clicked yet.