That behavior is correct.
The effect of Cultist will allow you to play any card named Cultist. But inherited Estates are not complete copies of the card they inherit. They retain their cost ($2), their name ("Estate") and they are still Victory cards in addition to the types of the inherited card.
That means once a Cultist effect executes, it will not see your inherited Estates (partially mimicking a Cultist) as potential cards to play; the mimicking was not perfect and the important part for the Cultist effect (the name) was not mimmicked.
OTOH, such an inherited Estate does get the ability of Cultist, so, as you noticed, an inherited Estate can start a Cultist chain, it just can't continue it.
Note that similar things happen with Outpost and Crossroads, cards that use their own name to limit the effect they have.