A warm bulb (around 2700K) shifts everything slightly toward yellow/orange; a cool bulb (5000K+) shifts everything slightly toward blue-white — the effect is on top of, not instead of, the wall colour's own undertone.
Neutral-undertone colours are the most forgiving across different bulb types, since they have less existing bias for a bulb to exaggerate.
A colour with a strong existing undertone can look noticeably different — sometimes muddier — under a mismatched bulb colour temperature.
Testing advice
Check a sample under the actual bulbs that will be used in that room, both during the day and after dark.
Lighting simulations and descriptions here are approximations, not exact physical predictions — see methodology.