Recently traveled with wife and 5 yr old. Lunch at MIA took forever.

Arrived at the gate where the gate agent was calling our names, waving frantically to us, and telling us he was ready to shut the jetway doors.

After we scanned our tickets, I checked my phone to find we were still 14 minutes out from departure time. I gave that piece of information back to him, and the other gate agent said, yes, but we were about to give up your seats.

Additionally, went into the jetway to find it completely backed up with people. Once inside, the gate agent took my son aside to show him the cockpit (which was awfully nice, but seemed to contradict just how pressed for time we were at the top of the jetway).

My question is - is there a specific number of minutes prior to departure that the Gate Agent can start giving away confirmed seats to others such as standby?

Thanks!