World of Kulan DM
Okay, I have this sense you're trying to convince me that the choke point is wide enough that Tim shouldn't have to squeeze through. For now, he's not in combat, so it doesn't really matter. However, if combat breaks out and he has to go back through the choke point, you will have to use the squeezing rules.
I looked them up specifically to try to figure out if he would have to or not using tactical movement, so I'm certain if the smaller area that Tim is occupying isn't as wide as the normal space (not the size of the token) he takes up during combat, he has to squeeze through. Remember that for combat purposes, the space a character takes up is defined as "the amount of floor space a creature requires to fight effectively" (PHB, p. 312).
Tim's not in combat right now, so don't worry about it if he doesn't have enough movement to get him to where you want to put him if there was combat. We'll only worry about it IF I call for an initiative roll. ;D