When should a chest tube be removed during the ventillatory cycle?

That's Debatable: Some surgeons remove it at end expiration, reasoning no air can rush in then. Others remove it at maximum inspiration, since there will be no opportunity for air to enter. It likely doesn't matter which of these is chosen, the important concept being not to remove it during inspiration when air could be pulled in through the incision.

At end inspiration : The patient should fully inspire to the point he/she is unable to breath in any more. Therefore, there is little risk for sucking air into the chest cavity during removal. Some people teach removal while exhaling (this creates positive pressure in chest). The risk here is that it is natural to breath in when experiencing pain. Thus, patient has more risk because he/she can suddenly suck air in.