Think of it as a compensation for the color of the light. You have a neutral gray on a print built from a D50 profile which appears neutral. But if you placed that into D65 which IS cooler, what would the effect be? The gray would look cooler, not neutral gray. So the new profile compensates for that. If you build a profile for that cooler illuminant, such that the gray would not look cool the profile has to adjust warmer. And that's what I see when I view the two side by side. The higher standard illuminant value compensation looks warmer to adjust for it being the cooler appearing illuminant.
We see the same behavior with Lightroom's Tint/Temp sliders. Move Temp higher, the image gets warmer.