TIL lists 414 as the date of the opening of Vvardenfell to settlement. Now, Vivec City could have an exception, but I like to ignore this date entirely because it is far too recent. If all the settlements are that young, the quality and believability of the setting takes a hit.
In 3E 414, Vvardenfell Territory, previously a Temple preserve under Imperial protection, was reorganized as an Imperial Provincial District. Vvardenfell had been maintained as a preserve administrated by the Temple since the Treaty of the Armistice, and except for a few Great House settlements sanctioned by the Temple, Vvardenfell was previously uninhabited and undeveloped. But when the centuries-old Temple ban on trade and settlement of Vvardenfell was revoked by King of Morrowind, a flood of Imperial colonists and Great House Dunmer came to Vvardenfell, expanding old settlements and building new ones. - http://www.imperial-library.info/mwbooks/short_morrowind.shtml
It was open, sorta, just not to the Empire. So Balmora, Ald'Rhun and Tel Mora were probebly there already and expanded greatly in a few years.