I don't see the removal of Sotha Sil from the mortal plane triggered the invasion. Mehrunes Dagon chose the time to attack the emperor because the imperial legion was spread so thin. The death of the emperor to the hands of the Mythic Dawn had been in planning for centuries and Sotha Sil or not, it was still going to happen and the removal of the barrier would've still happened without the dragonfires.
Yes, indeed, they had been planning for centuries, gathering followers, Camoran fueling his paradise with the continuous death and resurrection of the people trapped there.
They were biding their time, until ancient prophecies came to pass.
The fall of the red tower and Sotha Sil.. well, hatever happened to him happening, he could just be in the timeless god-place but unable to manifest on Tamriel.. Anyway the barrier between oblivion and Tamriel was significantly weakened.
Not only because the connection of Lorkhan's heart to Nirn was severed, but also because of the pact Sotha Sil made with the Daedra. That pact was still in place, but with one of the parties who made it no longer a presence, less powerful.
Or, the pact could have just been for a measured time to begin with, and the price to pay could have been what actually happened.
This event was what Mancar was waiting for.
With the red tower gone and the barrier weakened, he could attack another tower.
The Septim lineage and the amulet of kings.
Only when those two towers had fallen could oblivion gates open.
So the events of Morrowind are a necessity to those in oblivion.