What are your settings? Are you using AWB or are you toggling?
The best way to get it done in your environment is to make sure that the camera is calibrated to your lights.
Quick Way: Grab a gray card, it's like $5. Then stand with the gray card in your frame... from there you can shoot the gray card to set an custom white balance. Save that white balance. Now when you're outdoors or in natural light, use that white balance.. when you pop your studio lights on, use that setting.
You can also color grade your video. That's a whole other science and topic that I'm definitely not equipped or knowledgable enough to speak on. Look up Matt Lutts and go down the rabbit hole of color grading techniques.
