In my experience it is important to not just tighten the locking tuners but also give a small turn with a flathead screwdriver in order to keep the guitar in tune. Also some lubricant in the nut slot can really help and stretching the strings and tuning after using the tremolo bar is very important. PRS send me a document with some info about the trem and tuning:
"
Understanding tuning stability and the PRS tremolo
The PRS system works in such a way that any flattening of strings due to bending
can be reversed with a sharp dive of the tremolo; you can hear this clearly for
yourself if you do a big bend on the G string at the 12 th fret – the G string will go
slightly flat and some of the other strings may go very slightly sharp to maintain
equilibrium. Give the tremolo a quick dive and it should all return to somewhere near
perfect.
If you don’t follow the resetting rule above the tuning can appear to go haywire as
the following scenario plays out: you do a bend, the string goes flat, you re-tune it
with the tuner and the next time you use the tremolo the unused reset effect makes it
goes sharp.
The golden rule is to always tune after you have dived the tremolo and not directly
after bending. For this reason, any time you re-string your guitar you should stretch
each string, give the tremolo a dive, tune, stretch, dive & tune again. Have a look at
this clip of John Ingram, one of the original factory techs, talking about setting up the
PRS tremolo:
Relevant part at (3.32)
Additional information about setting up your PRS is available here:
https://support.prsguitars.com/hc/en-us/categories/4407425254427-Electric-Guitar"