Harry Connick Jr. is playing for an audience of squares, and they're all clapping on the 1 and the 3. A lesser musician might just accept it, but Mr. Connick is a Jedi, and fixes the problem without the audience even knowing what's happening.
Watch from about 0:30; the transition happens at 0:39. In particular, check out the drummer's reaction when he cuts over the beat.
There's probably an Aikido metaphor in here somewhere, but I'm not sure I can describe this level of mastery better than the eloquent youtube commenter lavi:
lmao fuckin sick how he throws in that 5/4 bar so smoothly to fix the clapping -