Probably too taken aback anyway by how 'starting tonight' became the middle of the day (1300 hours).
Yeah, looking back at the particulars, Jellico kind of sets Riker up to fail. He says to have the new shift schedule starting "tonight," and then expects it to be fully implemented prior to the change-of-command ceremony. Riker seems to have been perfectly reasonable in expecting that either at the CoC ceremony or their meeting a couple hours at 1300 later he'd be able to run the concerns with the shift change by Jellico to get more specifics on the trade-offs he was willing to make and still have time to implement the new rotation by, let's say, 1800.
The question is, would it have worked if Jellico hadn't decided to pop off a probe to help Picard, or, alternatively, if he hadn't micro-managed Riker by specifying exactly which shift would actually be launching the probe in his order. Ironically, that's exactly the kind of mixed-messaging that creates conflicts. Jellico is expecting Riker to "get it done" hours ahead of deadline with a very complex and broad order that requires a lot of detail work it would be reasonable to want the new C/O's input on, but gives a needlessly specific order that's dead simple and didn't need the level of explication he gave it. If he'd just said, "Make sure a probe is launched just before we drop out of warp," Riker would've had the chance to bring up the problem during the meeting and say, "Hey, we can either have half the crew at their stations exhausted now if we go six on, twelve off, or we can have them all exhausted later if we go six on, six off, or we can have the ship undercrewed if you want to go six on, eighteen off, which I'm pretty sure isn't what you meant given your context-clues are inconsistent with increasing crew downtime. What'll it be, skip?" and still have four hours to build the final schedule and work out the transitional period, rather than Jellico cracking the whip and ordering the transition to begin at 1500.
(I actually had a whole thing I deleted about Jellico not even being able to guess who would be on duty when under the new rotation before I decided that it was probably just SOP that a three-shift ship would rotate at 0000/0800/1600, and a four-shift system would rotate at 0000/0600/1200/1800, but since Jellico says like it should be obvious that fourth watch will begin at 1500 before it even exists, I guess I was right the first time and shift changes are up in the air. On the other hand, I remember reading a blog post that proposed TNG-era Starfleet didn't operate on the same kind of scheduling we do in the present day given the ample amount of free time to pursue expert-level hobbies the crew has, and maybe they aren't "at work" eight hours a day, but their duty shift is more like being "on call." I wish I could find it, but it was a long time ago).