In the case I'm talking about it was less about string tension and more that the guitar felt stiff. Very stiff. The rod was way tighter then it should have been loosening it and giving the guitar a few adjustments (trem claw, saddle height, etc...) really made a difference. It felt like a completely different instrument.
YMMV
There is a potential truss rod impact on string tension, but it goes the other way round. You switch from 9s to 10s, consequently, the strings put more pressure on the neck. The truss rod may then be too loose. Consequence : excessive relief, which may cause slightly higher tension on fretted notes.