In chapter 90, the sunbae confirmed with Moondae that he also went back in time. Since the sunbae went back in time much earlier, he encountered the missions first and is assuming Moondae has the same system so he is also assuming they both have the same missions which is true.
Moondae didn’t explicitly tell him about the missions but he also didn’t tell the sunbae that their systems were different and that he can see the status screens.
So the sunbae had to literally repeat and die over and over to figure out the missions in the first place, while Moondae had the status screen telling him the missions.

Which scene does moondae slipped up that give away his mission to his sunbae? I tried reread few chapters even before the variety show scene between him and his sunbae. But i still cant figure out how his sunbae figure out about the mission ヽ(`Д´)ノ