I was going to suggest that maybe the hotshoe flashes aren't putting out as much light on the walls. The shirt on the boy looks much whiter and is closer to the flash. The studio flashes have a higher output so would make a larger area whiter. It's basically an underexposure issue, I think. Not your problem, but the flashes not being powerful enough to reach the walls, just the subjects. Since the walls are a large area of the photo, it makes our eye see it all as purple, but I think if you crop way down to parts of the shirt and the woman's hair that they look much more white.
I don't do as much color, so take this with the usual grain of salt.