Pin setting and string equalization is two different things.  For years
I was doing it wrong.  I could not understand why, during a pitch raise,
I was ending up with each octave flatter and flatter as I went up the
scale.  I was tuning the piano to itself after setting the temperament
with an electronic aid.

What was happening was that as the strings were being pulled up, the
part of the string that was kinked around the upper bridge pin was
being pulled up into the speaking segment.  Once this kink was free
from the pin, the tension straightened it out, causing the pitch to
fall.  This was what was causing the flat treble, as the mistake would
become progressively worse with each octave.

So I decided to set the temperament with the electronic aid (a Borg
tone generator) then tune the upper octaves beatless to the aid.  This
eliminated the flat situation.

During the pitch raise, I don't bother setting the pins nor equalizing
the strings.  In the last pass, the temperament is set, and then piano
is tuned to itself.  I will bring the string slightly sharp, then
"pound down" (equalize) the string, while setting the pin.  On most old
pianos, setting the pins is an non-issue, because there is far less
internal torsion.

Tuning the bass correctly is critical to how that piano will "present"
itself.  Usually, there is a "correct notch" you can hear with most of
the bass strings, and is usually leaned a little toward the flat side.

Andrew Taylor