Active Duty Army here to give you some perspective.
After I signed my 199 and it was sent up, took me about a day or two to receive confirmation that I was put on the TRANSPROC list. Transition Services will give you a NLT of when you need to be out (this date can be tentative).
I unfortunately got stuck on a Jury Panel for 10 days in February and took almost an entire month of leave in March, but as of 27-March-2019, my Commander and I finally sat down to gather and send the required documents being asked of me back to Transition Services. Today, 28-March-2019 I received my orders. My Commander asked my opinion on a date of when I would like to be out. I went ahead and told him 13-May-2019 because this was the same date that reflected my NLT received back in February. My orders received today reflect the date of 13-May-2019.