The appearance of the "buttons" is simply a video creation that is part of the movie file that is playing in the background of the motion menu. They are not really buttons. But, they display the text and other aspects of what the user will see as a button. The background video can fade them in, and out for that matter; but generally they fade in and stay.
The Encore menu will define a "loop point" at some number of seconds into the background movie, and when that point is reached, the button highlights (and the link functionality of the button) become active. Up to that point (and even if the buttons "appear" earlier), the user cannot click on the button area and go to a linked movie. Once the loop point is reached, links can be clicked/selected by DVD remote.
You generally take the Encore menu you are patterning, place the still in After Effects, and animate/add video, but at some point in the video, you get to the exact position of the menu. That is important so that Encore has the highlights placed in the right location.