I am a visitor in the US on a J1 visa.

I want to transfer my Visa from Institution A to Institution B. Do I need to be physically present in the US so that this transfer can happen?

Suppose I leave the country, would I need to show up again within a certain time frame? By comparison, I know they only let you enter the US within the first 30 days of your J1 start (since you must report to your institution), but is there anything similar with J1 visa transfer?