I don't think the exact layout of the Section offices adjoining the time shafts is described. However it's clear that when they leave the kettles they enter some form of office that is still outside Time. To get into Time they have to pass through a curtain. For example in chapter 1 there is the description:
He paused again at the infinitely thin curtain of non-Space and non-Time which separated him from Eternity in one way and from ordinary Time in another.
This would be a completely new section of Eternity for him. He knew about it in a rough, way, of course, having checked upon it in the Temporal Handbook. Still, there was no substitute for actual appearance and he steeled himself for the initial shock of adjustment.
He adjusted the controls, a simple matter in passing into "Eternity (and a very complicated one in passing into Time, a type of passage which was correspondingly less frequent). He stepped through the curtain and found himself squinting at the brilliance. Automatically he threw up his hand to shield his eyes.
In the Hidden Centuries the Eternals still have access to the offices adjoining the time shaft, but they can't pass through the curtain to get into Time. In chapter 3 Asimov says:
The doors between Eternity and Time were impenetrable. Why? No one knew.
But I don't think he elaborates further, or at least I can't find any more details.
Anyhow, the occupants of the 70th to 150th centuries are presumably living in their time just as everyone else is. It's just that the Eternals can't get from the time shaft into their time.