As others have stated, it can vary, but here are the times based on colors:
Self-assist: 8:15am
Light Blue: 9:00am
Purple: 9:20am
Orange: 9:40am
Pink: 9:50am
Brown: 9:50am
Green: 10:00am
There were a couple other Red categories, but I believe those were for people who had excursions or shuttles to the airport.
Our self-assist on Thursday started earlier, but there were a ton of delays announced. We had Pink and didn't get called to go until 10:30a. Semis were blocking the access road for pickup/drop-off only allowing 1 lane of traffic at the port. It was a mess. I had to go get a car and come back to pick up my family and waited in line for 45 minutes (exit for Terminal 10 to the pick-up point; approx 1mile distance ).
We also learned they close the stairwells past 7th floor, so we couldn't even take the stairs down to 6 to go to breakfast in the morning (7:15am). Knowing what I know now, I'd plan for light blue and get to breakfast when they open at 6:30. Disembarkation was an overall terrible experience (mostly NCL fault, but partly outside forces)