USA mechanics question

[Tru_in_Blu]

USA slow pitch game, 2 umpires.

Bottom 7, tie score, bases loaded, 1 out. I am on the bases.

Batter hit a semi-line drive to the left of F7 - he had to move about 4 or 5 steps to get to the ball and caught it.

I started inside from "B" watching R2 to see if there was a tag up, and there was. (Frankly, I paid no attention to R3 on first.)

PU made the out call on the catch and I saw him starting up the line towards 3rd base. The runner that was on third apparently tagged up and headed home. The throw from F7 went to 3rd base where there was a fairly close play and PU called the runner safe.

As I started coming inside and saw things unfolding in front of me, I had a brief thought about if the out was recorded at 3rd, who was going to determine if the runner that tagged up from 3rd crossed the plate before the out was made. I did try to take a look, but it would have been tough to tell.

I think we covered the play correctly and all was moot when the runner was ruled safe at 3rd.

Back into the Umpire Manual, I was looking up the situation for when bases are loaded and fly ball coverage. PU is responsible for the tag up at 3rd, any play on the lead runner at 3rd, and any play at the plate.

I view the lead runner here as R1 on 3rd base at the start of the play. The definition does not seem to include responsibility for R2 from second base, except for the BU being responsible for the tag up there.

BU is responsible for any play at 1B, 2B, and the last runner to 3rd. So who is responsible for R2?