In MW they were "arising" religion with foothold in only few places around the place while in Cyrodill they had their time to sat on their butt and be lazy, they were main religion of the area.
In MW Temple's attitude towards Nine Divines could also have given bit more energy to Cult's actions. I remember that Triune, ancestors and even Daedra were seen as much more active and helping force than absent Nine Divines. So maybe Cult tried to prove Temple and rest of Dunmer wrong.
That's a good way to explain it. Expats often uphold tradition of the old country much more than those who stayed behind.
Cyrodiil was a land of plenty for the Imperials since they controlled all other provinces. Imperials and other westerners were a minority in Morrowind and as such band together they often band together in institutions they know from the old country.
In a similar way, it is interesting how the Thieves Guild was 'allowed' by the Legion, even going as far as allowing them to run Inns near Legion enclaves like Sadrith Mora or Ebonheart.
In that way it seems more of a ploy from imperial government to protect Imperial and western-tamrielic populations from Dunmer run monopolies and institutions where people from the west weren't allowed. Something which obviously wasn't an issue in Cyrodiil. In fact, it seemed there weren't even glass ceilings for non-western non-imperial races in Cyrodiil.