At least in AE, I'd prefer "past nine months" if that changes your understanding of the "signal word" (which I know little about). (I'd say that your form of the verb is correct.)

I'm wondering, though: Is that the use of "last" that really is a signal word for the simple past? (I could see it as "He worked there last year.")

Ok, thank you both very much for your help! He has left the job and moved, so the right tense would be simple past. Thank you as well for the help with "past" instead of "last"! :)