@ma_ko it isn't about believing that there might be an attack he knows enough that likely either there is something or that he is trying to create a diversion from something else. The problem is not somewhat trusting his information it is trusting him. From the perspective of people who don't know about time travel there are three options I can think of for how he got that info:
a) he just somehow overheard a secret plot, seems unlikely and he could have just told them if it was that.
b)he is connected to an organization with a good intelligence network. Not an official agency or they could give the info through official channels, so something secret. A secret organization that sends a group of young adults to transmit it and request to take part in the defense and to be let in the room of the item that is supposed to get stolen and they were let in that is rather trusting. And after the guy reveals his purpose was to play a game of chess with the leader of the tower. That isn't just some random student there is a plot there but what? Just establish contact? Couldn't his organization do it some other way? If it is supposed to be a discrete contact they did it in an awfully attention grabbing way, if attention grabbing was the point why did they want to grab attention? And he could have other purposes in his meeting, maybe the goal was a suicide attack against the tower leader, maybe the game is just a ruse and he just needed to get into their headquarters for some reason. Point is if there is some secret org behind him they revealed and handled it this way for some reason and they have no idea what that reason is.
c) Probably the one most think of first: He is directly connected to the criminal org that is attacking. Maybe he is a member who got an attack of conscious? If so that is good but you want to question him, the police will want to question him for more information and if he is connected he probably has committed crimes before that would also be of interest. Or (before the attack) he is connected and still works for them and getting him in there is part of some plot. Or (after the attack) he still works for them and the meeting with the tower master is part of some plot.
Basically we have some random guy who won't reveal how they know about the plans of a criminal organization so is likely connected to something shady or at least secret and the way he deliberately wanted to be involved in the defense (note that he only told them when there was little time left making it more likely they would need his help) and now wants access to a very important person indicates he is planning something. Just a tad suspicious.
But agree with the two that are saying that it might be better for the author to leave it a plot hole because it might be beyond the authors skill to handle it well.