"The director is going home then I am going too."

Does "o zaman" mean something like "so" or "in which case", i.e. "The director is going home, SO I am going too", or is it meant as the second part of a conditional clause, i.e. "IF the director is going home, THEN I am going too", or does it mark part of a sequence, i.e. "FIRST the director is going home, THEN I am going too"? The meanings is similar, but not quite the same, and the English sentence is somewhat ambiguous as a result, so I'm having difficulty sussing out the meaning of "o zaman".

I would say that "o zaman" does mean "in which case" and doesn't really work here. It suggests causation.

I actually used "ondan sonra" (after that) because in this example "then" is referring to a chronology, but it was graded wrong.