Inning ending mistake

[Little Jimmy]

One of my umpires described this situation that happened to him today. He wanted my opinion and thought I'd throw it out to you all. R1 on second. As the B2 steps up to plate my collegue checks his indicater and can't recall if there is one or two outs. Before he can signal to ask his partner the B2 hits a fly ball to center. F8 catches the ball and runs in as defense and offense start to change sides. He says to himself that must now be three outs, goes in, sweeps off the pitchers plate and goes out past 1st to await the new inning.

Defensive coach from a few moments ago now says, wait a minute, that last catch was only the 2nd out. He wants to appeal the runner at second for not tagging up. Umpire confirms with both books that there really was only 2 outs, and decides to put everyone back on the field and keep R1 at second base for no specific reason other than it seemed like the right thing to do.

I'm not sure what the right call is. The inning had not officially ended so I think the appeal would be good. Maybe an out for abandoning a base could be in order. Putting everyone back doesn't seem right but I don't know a rule that covers this. What do you think?