HS is the only "Required" age to go to -3 unless you are playing Dizzy Dean league ball (13U). Players start transitioning to -3 around 13U or 14U in preparation for HS, depending on when they enter HS (as a 14 year old or 15 year old).
I would recommend at 13U to at least get a -3 wood bat to hit with in the off season (many places have scales to weigh the true weight) to start getting used to it. Make sure you weight it to know for sure. Depending on the model, they can be anwhere from 0 to -3.5. My son has a -1 that he swings in the off season that makes the -3 feel lighter.
I see a lot of kids go to -3 no later than 14U because the pitches are slower because of the move back 6'6". It seems like a good year to transition.
We play 13u and to the best of my knowledge No tournaments require them. But we have some kids on our team that play middle school ball and they are required to use -3. We also have a kid thats playing 14u rec ball and they are required to use -3.