So Passpartout says the time by his watch is 11:22 and then Fogg says it is 4 minutes slow, making the time approximately 11:26.
If the time was actually 11:22 by Passpartout's watch, there woould be a 50 percent change the watch said the time was less than 30 seconds after 11:22 and a 50 percent chance the watch said the time was more than 30 seconds after 11:22. So maybe Fogg assumed that Passpartout's watch said 11:22:30, And that Fogg's watch, or his clock on the wall behind Passpartout, said a time between 11:26:30 and 11:27:30 and Fogg said the difference was 4 minutes because it was more and 4 and less than 5 minutes.
That would make the time when Fogg made his statement between 11:26:30 and 11:27:30. And when Fogg later said the time was 29 minutes after 11 the time might have been between 11:29:0 and 11:29:59. So there would have to be between 1 minute & 30 seconds and 3 minutes &29 seconds.
Could there be that much time between those two statements of Fogg's?
If not, here is another suggestion.
Maybe Passpartout looked at his watch and it said 11:22:58 and Passpartout said 11:22. And then Passpartout turned his watch so Fogg could see and by then it was 11:23:02 and Fogg considered the watch to say 11:23:00 to 11:23:59 . If Fogg's own watch said 11:27:00 to 11:28:58, he might consider the difference to be 4 to 5 minutes and say four minutes. and if his watch or clock said the time was almost 11:29, Fogg might think that by his acceptance of Passpartout's services the time was now after 9:29 - or maybe Fogg looked at his watch or clock again and it said the time was now after 11:29:00.
And if that seems improbable, here is a third suggestion.
Maybe when Passpartout showed Fogg his watch giivng the time as 11:22, Fogg looked at his own watch (in need of winding) and it said 11:26, so he told Passpartout that Passpartout's watch was four minutes slow. But when Fogg accepted Passpartout he naturally looked at his super accurate marine chronometer hanging on the wall and saw the time wass 11:28:50 and told passpartout "No matter. Both our watches are slow according to my Marine Chronomoter." And then Fogg decided to hire Passpartout and looked at the chronometer again and it showed 11:29:10 and Fogg said: "It is enough to have mentioend the difference. Now from this moment, twenty-nine minutes after eleven, a.m., this Wednesday, 2nd October, you are in my service.”
But then revising his MSS, Verne crossed out the line "both our watches are slow according to my Marine Chronomoter." Or maybe the typsetter omitted it by error when setting the time, and nobody noticed it was missing.
Or maybe Verne used Arabic numbers for the times in this scene, and maybe the typesetter had trouble distinguishing between "2" and "5", or between 4","7", and 9" and selected the wrong numbers or letters when setting the type.
So here a few possbile ways to think that Verne might not have made a simple error in arithmatic.
Here is a link to a question I asked about a story where a literary critic was obsessed about an uncertain detail in in a story, and eventually used time travel to asked the author.
https://scifi.stackexchange.com/questions/128745/time-travel-for-literary-research-from-analog-c-1990s
And if your research doesn't give a definative answer, and time travel is invented, maybe you can go back and ask Jules Verne. And maybe he will explain why that scene is correct. Or maybe he will say howstupidhe was to make such a simple arthrmatic error and not catch it will revising. People must have thought he was an idiot for centures. Andmaybe you will say you were the firstperson who ever noticed it in a 150 years - which might be true for all I know.
And just in case you are the first person to be bothered by this detail, congratulations!