If Jellico wants a four shift rotation he has every right to it, even if it is unusual. The crew don't have the right to ignore the order.
Jellico has his reasons, and they are probably sound given his command experience. No one condemns Commander Adama on BSG for refusing to network computers despite it being considered at least as idiosyncratic.
Its worth noting that Jellico is preparing for a very specific mission, one that he actually expects to fail hence the lack of confidence Troi detects - it alway struck me as odd that we are supposed to see this revelation as putting the man in a bad light given the circumstances. Along similar lines as he says, given the mission they are on he has no time to be touchy feely in his change over. He expects he is going to have to take Enterprise into combat and wants to be prepared.
While his command style would be different to Picard there is nothing to indicate that Jellico would be so hardnosed if the situation were less critical.