This is a good point. MC, or more importantly, I made a huge mistake here, in revealing Mason to Tom, or letting him keep the memories of the encounter. I think I'll edit it, so Tom doesn't remember the exact relation between himself and Harrison, only that they're related. And even the name, I think. Sorry for this.
Author it's perfectly fine. As long you have sufficiently plausible reasoning for your decisions or a willingness to listen to people like me bitch at you, then it's fine.
So summarising the problematic points for me (and I believe quite a few other people) in this latest arc:
1) MC wanting to be a medic. There seems to be bit of a disconnect here. A disconnect between you telling us the MC wanting to be a 'save as many as you can' kind of doctor, and the pragmatic kind of doctor you are building him to be. Initially I thought him being a doctor, was just another step in his journey and mainly about adding medical skills to his repetoire. But somewhere along the line this suddenly became his dream(?), or it jumped a lot in importance to him. To me this situation felt a bit abrupt, considering his actions thus far in training his 'strength' and how hard he was training for them.
He's putting all this effort into learning medical skills, even going as far as to register in a normal medical school (which considering the knowledge available back then, was definitely lacking compared to the magical version, so a bit pointless) to actively seeking a military role in a manner that came across as bit of battle/adventure seeking junkie? And thats not forgetting the fact that most of people he is going to be forming bonds with in his training will probably come back in a casket. It felt like he was taking things too lightly. It was just a switch that was quite abrupt. Plus his reasons for joining the war (meet Steve?) are generally very unclear and unsatisfactory for a perceived doctor.
2) The oath itself. Knowing what he knows about the future of Marvel, restricting himself for little gain seems very foolish. There are plenty of other ways to help/save people without becoming a magically oathbound hospital doctor. Even if he got one with a bit more leeway, it just felt like authorial fiat making sure MC will have sufficient drama and conflict to be 'challenged'. IMO it feels like this is a bit of overcompensation from your other fic since that one became OP too quickly? I'm not sure.
3) The entire Tom debacle. This was handled very badly IMO. There is almost no way I see them meeting, without Mason killing him, to be logically consistent. Because right now he's pulling off a terrible light novel/anime trope of letting someone go due to *insert cliche/terrible reason* so they can come back later stronger and better prepared to have a better match. Even with the oath, seeing someone carrying a weapon with intent to torture/kill (confirmed by mind reading) is absolutely reason to take them out. Even more so after they had just attempted to do so to your person. You don't see someone with a aimed gun and a finger on the trigger then wait for them to kill someone before you act.
Also giving any kind of identifiers (name, skills, age etc) is a bad idea. Especially since MCs alter egos aren't fully independent of each other and there do exist connections that can be found.
There's a bunch more reasons the Tom section was problematic but the others have mostly covered them.