Add time delay before layer is visible

For delaying things, you can use cue points, or you can split things up into different slide layers to only make them happen when the user goes to a slide layer.

You can right click the timeline and choose Create Cue Point at Playhead. This is like a bookmark in Captivate. Then, you can use a trigger to pause the timeline when the timeline reaches the cue point. Then you can add a trigger to resume the timeline when something happens.

If you are dealing with 3 buttons and you don't know where the user will click, you might want to separate things onto 3 extra slide layers, if you haven't already. Then, you can control which layer is seen with which button, and add transitions to the layers. You can divide what will be seen at different times onto different layers.