In multiplayer (and not in singleplayer), when you paste within the copied region, the pasted content also becomes part of the clipboard. Depending on the direction of the offset, the new pasted content can then be pasted again.
Actually this is the way it works. It's a TODO to expose this difference by providing different graphics and text labels. I even drew some icons but they were ugly
and I didn't include them, yet.
In multiplayer, the tool works like you said:
copy -> select area to copy/paste
paste -> copy current
content of area selected previously with copy tool and paste it instantly at given location
There is no need to synchronize anything
over the network. Otherwise each player would have to poses it's own copy of all other player clipboards. Another solution would be to send clipboard over the network while pasting which is also problematic. Current approach is really bug proof and functional. And enough for players IMO. Do you think otherwise?
My preferred solution would be to send the clipboard over the network while pasting, as this is required to implement save & load functionality for multiplayer games.
Furthermore, the current solution has at least two bugs. One is your TODO. The other is that pasting once inside the copied region (in a multiplayer game) can cause the contents of the region to be pasted multiple times.
For example, if you copy  ('.'=grass, 'D'=depot) and then paste it one tile to the right, you get  instead of , which is what I would expect. Furthermore, if you pasted it one tile to the left, you would get .