if the tournament has started then you can finish it, if not then i beleave you'll be relocated to the correct tournament (only for the official chess.com tournaments though)
What happens when my ranking improves above tournament guideline?

For official tournaments: "If you register now and your rating changes before the start date, you will be AUTOMATICALLY moved to the correct group when the tournament starts.". See the area above the comments. There is no need to move yourself to the correct group. Just stay there and watch the comments of people complaining about you.
For member-created tournaments there is no impact. The tournament director could manually remove you, or you could withdraw.
Am I still eligible for a 1200-1400 tournament if my ranking improves beyond 1400 afterI've joined ... my ranking was 1240ish when I signed up.