Delayed Asking For help.......

[Chess Ref]

I'm PU. Deep grounder between F5 & F6. Shortstop comes up with it and throws to 1B. I'm moving up the line. We have a close play. BU comes up with strong out. I see the pulled foot. Everybody's hooting and hollaring but nobody goes to my partner. Girl goes into dugout, next batter approaches, then offensive coach asks for time and goes to my partner. They talk and coach goes back to coaching box. After the inning is over partner comes over and explains the reason he didn't ask for help was cause the player entered dead ball territory..so she was out either way.

What say you ? Is this correct ?

Also had runner on 3B. Line drive shot to F5. Catch and pretty close play on R1 scurrying back to bag. Partner believes I should have call but I believed he should have call. In the Umpire Manual it says first play in the infield by an infielder on a batted ball is taken by BU. What say you ?