The "flashback in a dream" scenes from Divided Loyalties, in my opinion, are no reliable sources of information about the Deca OR the early lives of the Doctor, the War Chief, the Monk, the Rani, the Master, etc.
There's a rather massive continuity error:
In The Time Meddler, the First Doctor does not recognize the Monk at all. He gives absolutely no indication that the two have EVER met before. So already, Mortimus/the Monk and the Doctor being school buddies makes zero sense because if they were, the Monk would recognize him (and the Doctor probably would too). But they don't.
It's also noteworthy that the Master is referred to as "Koschei", as if that's his actual name. Which doesn't make a lick of sense whatsoever, given that he only started using the name in The Dark Path. In that, the name is an alias.
Essentially, the dream that has a "flashback" to the Doctor's school days with the Deca shouldn't be taken at face value. All information originating in that part of Divided Loyalties should be noted as potentially distorted accounts of the truth, because it's explicitly stated to be a dream. Some elements could be completely wrong. Parts of the events depicted undoubtedly happened, but we cannot be completely certain what was the original series of events as the Doctor initially experienced them. Thus, I'm suggesting that information presented there be prefaced by a statement that the info comes from a dream and thus may not be 100% accurate.