Tiber gets Numidium from Morrowind. Tiber uses Numidium to aid in the conquest of Tamriel. Then, Numidium is destroyed. What keeps the Septim empire together? Tiber's greatest weapon is gone. Cyrus' rebellion is perhaps explicable in that it took place before Septim's conquests were consolidated, but in the ensuing decades Tiber was defeated by the Altmeri navy in his attempts to take the Isles. Essentially, Tiber was not invincible, and that's obvious. Is imperial rule sufficiently beneficial by the time of the destruction of Numidium that people want to be part of the empire?

Political dissents being quelled by the Numidium aside, Alinor was completely wrecked by the Numidium and had already surrendered, and given that Imperials had a foothold via provincial governors and the like, it would have done more harm then good. Given that Hammerfell already sued for more favorable conditions via Stros M'kai rebellion and Morrowinds own treaty, there weren't many forces at that point that could probably defeat Tiber without resorting to a long and drawn out war. Black Marsh is arguably the few places that weren't conquered in their totality, but there's no real point in that aside from gaining the few coastal cities throughout.

From a letter related to the Daggerfall quest Mantella Revealed:

"Numidium was Tiber Septim's secret weapon in his bid for supreme power: a thousand foot tall automaton, a golem or an atronach of sorts powered by a gem called the Mantella. The Mantella was infused with the life force of TIber Septim's Imperial Battlemage, and with it, Septim crushed all who stood in his way. After the complete and total defeat of all his opponents, Septim began using Numidium to crush the neutral royal families of Tamriel so that he could enthrone only persons he knew to be loyal. His Imperial Battlemage was furious at this use of his creation, and fought to reclaim the Mantella. In the ensuing battle, both the created and the creator were vanquished: the heart they shared blown out of this reality into the netherworld they call Aetherius. Numidium's body was scattered throughout Tamriel..."

It's not clear how devastated Summerset was by the use of Numidium, nor is it clear whether the Altmer knew the Numidium's body had been scattered. They may have thought that any rebellion they could muster would be swiftly crushed by it.

Anyway, it can be presumed that Tiber made it a priority to enthrone loyal persons in Summerset promptly. And about a century later, the Empire helped the Altmer repulse a Maormer invasion, which probably helped foster good relations.

Tiber used the Numidium to crush all royal families that didn't obsequiously except his reign. The reason why this action is barely known to the people of Tamriel (and in turn why Tiber isn't seen as a brutal tyrant) is because it happened during a Dragon Break, and events that occur during a Dragon Break are almost completely forgotten by those who experience them (save for people like the Tribunal or Shezarrines) once they end.