When I am a judge (mostly outside Virginia/DC!) here's what I do:
I go to the door, open it, invite the team to enter, and when everyone is through the door, I say, "Welcome to XYZ judging. I am starting the clock now."
Teams shouldn't expect a one-minute warning. I have a watch timer that beeps at the 5-minute mark. If a team is finishing up a project presentation, I'll typically let them continue a little bit, or I will say, "that's all the time we have for your presentation, Now we'd like to ask you some questions."
Note that it's rare when, as judges, we get as much time to talk to teams as we'd like to. However, although your team's next event might be 30-60 minutes later, typically there's a team waiting to come in to the judging room already, and as judges, we'd like to have a few minutes in private to compare notes about your team. So a prompt exit of the judging room when the session is over is welcome, and shows good Core Values by keeping the other teams on time for judging.
In Virginia-DC, the standard is that each judging session is 10 minutes long, from when the team enters the room until the end of Q&A. This may vary slightly based on tournament schedules.
VA-DC FLL Referee Advisor