Question about the law in my yeshiva

Hello Rabbi Michi.
In the yeshiva where I study, there is a rule that states that a man who does not enter the synagogue by the time the prayer begins (8:10), cannot enter afterwards. That is, let's say a man enters the "Zaal" at 8:14, the mashgih will tell him to leave and not to enter.
As a result, the young man will not be able to pray in the minyan at that time, because there are no synagogues nearby at all, and only if he gets on a bus to a nearby neighborhood will he be able to find a minyan to pray in, and then he will miss some of his studies, which begin about an hour after the end of the prayer, with the travel. The reality on the ground is that a young man who was banned from entering because of being late sits in his room and prays alone.
I would be happy if you could teach me the halachic opinion on the matter, because it seems puzzling to me that because of the prohibition against being late, it follows that young men cannot enter and pray. (Even if this means that they will be recorded as absent from the prayer, at least they will be able to enter and pray properly in the minyan.)
Is there a halakhic permit for a supervisor to prevent entry to prayer? (If applicable, the only one in the area)
 
Blessings on the reading.