I wouldn't find it unlikely for word to get to Tom about his cousin - maybe a non-Controller Sharing member might say something like "your cousin Phillip is such a weirdo!", if they had spent more than a minute with Ax :p
Though it could be hand-waved, maybe Tom might assume it's a cousin's of Rachel he and Jake don't share, or that Jake was lying about it for another reason.
I've worked in schools, and I find it hard to swallow that any stranger would easily be allowed in a school he doesn't attend.