Chef,
Your local visa office is the one in Kingston, Jamaica, right?
The answer to your question is NO. They don't give a time frame. But I guess with any local visa office, once they requested for your passport, they expect you to submit it the soonest time possbile.
In my case, I got my passport request first week of March. But at that time I was shceduled to travel overseas first week of April and be out of the country for almost two months. I decided not to submit my passport outright since I really don't know how long it will take them to issue the visa and send the passport back to me. But just to be on the safe side, I actually wrote a letter of explanation and sent it to the ambassy via courier (and through fax as well). I included in the letter my predicament (come up with something excusable) and informed them of the date I planned to actually send my passport to their office.
When I came back from my travel last week of May I sent my passport to their office and my visa was issued after about three weeks with no problems at all.