If you have a beat and have an instrument play off-beat, I have no idea if that is called something else. That is just part of the harmony because the melody is the dominating sound, anything else that is part of harmony.
Layering is from what I understand is when you are electronically making a sound. In an orchestral setting it's different.
How orchestral music works is that everyone had a different part. You either play melody and harmony. Within the melody and the harmony the parts are different. Sometimes instruments come in at different points in a song. If you are directly looking at sheet music of a song and compare the different sections, say like violin and cello, it will look totally different. A group of instruments may be playing while another section of the orchestra just have a series of rests. Now if there is a word for it, I can't think of it.
Really the better example of this I can think of on the top of my head that you are talking about is The Hall of the Mountain King by Edvard Grieg. [link] That is the best recording I could find but I've heard better. I played it, somewhat of a difficult song to play because not only does everyone kind of step in a moment and step out, but it starts increasing in tempo and getting louder.