Required Tag-up for Out-of-bounds Play

[TheElder]

With a runner (R1) on first base, a foul fly ball is hit to the Left Fielder. R1 is standing between first and second base and is waiting to see if the ball will be caught.

The Left Fielder catches the ball and then his momentum carries him across the out-of-bounds line.

The base umpire awards R1 second base. R1 proceeds to second base without returning to first base to "tag up."

Before the next pitch, the defensive team appeals that R1 did not tag-up at first base after the caught fly ball.

Question 1: Is R1 required to go back to first base and tag up?

Question 2: Is this situation an "appealable" play or a "correctable" play (i.e. assuming that R1 needed to go back to first and tag up, and the umpire "awarded" him second base, could the play be "corrected" simply by having R1 return to first base and resume play from that point)?