In many uses, "thereafter" and "afterwards" or "after that" have essentially the same meaning, and one can be substituted for another with no significant change in meaning or grammar. The word "thereafter" is perhaps a bit more formal, and more likely to be sued in giving instructions, or formulating legal documents. It is also more likely to be sued when there is an implication of causation, not just sequence in time. But all of these are at most tendencies, not rules. I can't think of a case where "thereafter" would be appropriate but "afterwards" would be clearly wrong.
The given example:
For the first month you’ll be working here, and thereafter in Chicago.
is fine. But since this seems to be informal speech, I think that the form:
For the first month you’ll be working here, and after that in Chicago.
would be more likely, and seem more natural, in US usage.