First..sorry about the way the read the book sounded...didn't mean it the way it "came out".
The ASA National Umpire School I went to this year they said PU has the play at 1B. Every ASA National I have done they say PU has play at 1B.
Add to that, page 182-183 of the manual under Leaving the Plate Area and Trailing the Batter-Runner states This will enable you (meaning PU) to either
make or assist the base umpire in administration of
7.
The base umpire going to the outfield. You are already in position to make any calls on the bases that may develop.
Also, althought I don't know if this is from ASA or not, but on Cactus Umpires (ASA) there is a document
http://www.cactusumpires.com/pdf/3-umpire-handout.pdf it states on page 3 section 3
When an umpire chases, we are working
with two umpires. Usually, but not always,
we revert to the two umpire system.
For instance,
when 1U chases with no one
on, P covers 1st and 3U rotates into 2nd.
When the BR advances to 2nd, P goes back
to the plate and 3U takes the runner to 3rd
if needed.
So that is why I am having confusion on the matter.