Sterling normally have 2 gate agents and a dispatcher. One agent has to remain at the entrance to the gate lounge to pull boarding cards, the second in a case like this would normally do "tarmac" - ie be on the apron making sure pax board the aircraft and don't wander off anywhere. The dispatcher will help if possible, but they usually have many other things to do while boarding is going on. If there were 3 gate agents, ideally one should have been at the exit to the lounge, however the third person you saw at the gate was probably the Sterling rep.
When boarding starts the tarmac agent will make sure the airbridge doors are closed, and lead the first set of pax down the stairs. If there are only 2 agents available, one HAS to be on the tarmac for boarding, so you just have to hope that the next lot of pax will follow the first down the stairs. However this does not always happen. Many times I have closed the airbridge doors, put the tensor barriers up, and even placed a bin in front of the doors as well, only to look up and find one passenger has decided they knew best, moved the barriers, opened the doors and gone down the airbridge!!! Once one does it, the rest will follow!
Did the boarding announcement mention that pax were to use the steps not the jetty?