I'd like to create a little map about colonization, that's why I'd like to animate a map and color it, just in the same way as this video:
That style of color overlay can be accomplished using animated shape layers and blend modes. You create the artwork, do the appropriate masking, then stack up the animated layers and change the blend mode to something like Color or Overlay or Screen or Multiply. The blend mode depends not he colors above and below.
If you do not know how to animate mask shapes or separate layers then let us know and we'll point you to some basic AE techniques tutorials.