After Effects question: How to create video similar to the one I have linked below

The Trapcide Suite from Maxon would give you better control over the burning maps sections of the sample animation. It's just going to take a lot of layers and a lot of keyframing. It could all be done in After Effects by an experienced professional in a reasonable amount of time. 

It could take a beginner a few weeks to figure out how to get all elements working to create the same kind of animated map.