Won't killing the first dragon at the tower start random dragon appearances? Or does finishing the quest activate that?
I also just recently ran into this problem without realizing it was there. Decided not to do either for the time being.
The wiki says finishing Dragon Rising will kick off random dragons. But I have not seen anything in the quest script that does so. Either I am missing it, or the wiki is wrong (or it got changed in a patch). I know for certain that A Blade In the Dark will start random dragon appearances, as the code in there to do so.
If you are on PC, you can prevent random dragon spawns just by opening the console and entering this: set MQ106TurnOffRandomDragons to 1. There will still be dragons at word walls, and the named ones that are part of the main quest. But there won't be the other ones randomly popping up everywhere you go.