Yet the best is to weld those edges before extruding (Push/Pulling) so that they won't cause any headache later. To check why it would be better, try these steps (now that you have the side facets softened):
Push/Pull the top face higher; fine, you cannot see any difference, the side is still smooth. Now Ctrl+Push/Pull the top face (this will create a dividing face in between) but now the unsoftened lines appear again.If you welded the perimeter first, this wouldn't happen.