I used to fly an ancient turboprop whose pressurisation was totally manual.
At rotation/liftoff the cabin VSI would always show a descent of 3-500fpm before showing the same ROC as the ac by about 2-300' agl at which point we would inch the 'spill valves' closed to introduce supercharger air (Nb not compressor air).
I guess the pre-pressurisation is to avoid this sudden cabin descent on t/o.
Cheers all
mcdhu