Here is what Ken Rockwell says. What he is basically doing is filtering the strobe light to match the ambient FL light temperature.
"If you change the white balance to tungsten or Fluorescent the backgrounds will look normal, but now the fill light on the subject will look blue or purple. Not good.Here's the trick from Hollywood: you need to gel (filter) the flash to match the ambient light and then set the white balance for that ambient light. Now everything will look normal. You could gel all the ambient light to match the flash instead, but that's a lot more work since there's a lot more lights. In Hollywood movies we'll spend a day gelling all the different kinds of lights and even gel set windows to make outdoors match tungsten. (The funny part is Hollywood is still based on gelling everything to tungsten, since that's the film we shoot, but almost no lighting is tungsten anymore.)The best place to buy gel filters, which are just colored sheets of plastic, is your local theatrical stage and lighting supply store. They are a couple of feet on a side and cost a few bucks each. You cut them with scissors and tape them where you need them. Popular brands are Roscoe and Lee. You can get a free sampler from these stores to try out which color works best before you blow a whole few bucks on a full size filter. In the stage world we worry about selecting from among the hundreds of colors they offer. Get the book for cinegels color conversion and correction filters."