Why does the light turn purple when I take a photo? (Read description)?

First thing to get is that your camera's sensor and your eyes do not see color the same way. Therefore you will likely never have a photo with exactly the same colors as you saw it with your own eyes.

A few things to check:

1) Is your monitor properly calibrated?

2) Was your camera set to the proper color temperature?

If you answered yes to 1 & 2, then it's the sensor in your camera.

A sensor in every camera is comprised of pixels - you know this. There are red, blue and green pixels, usually distributed in what's a called a Bayer pattern. This is the most common way of designing a sensor as opposed to stacking a red, blue and green sensor which, I think, is what Fujifilm does with their cameras. But back to the Bayer pattern. In this type of array, the green pixels occupy 50% of the total number of pixels, while the rest of the pixels are evenly distributed between red and blue pixels. It's because of this uneven distribution that you're experiencing false colors.

You could try shooting in RAW and then adjust the color temperature in post. You may also want to consider using a Color Checker Passport. This little guy is a plastic clam-shell that opens to expose an array of color pigments. You place the open CCP so that it has the same light falling onto it as does your subject. Take a shot. Then in post using the CCP software, the app then compares the colors of each swatch to what it knows that it should be and color corrects the image so that you get perfect (or as perfect as can be) colors.

I would strongly suggest that you do NOT shoot in JPEG mode when photographing under these lighting conditions. Instead, shoot RAW because RAW files provide you with the ability to fully color correct an image while JPEGs do not. For example, shoot a RAW image outside under daylight conditions while the camera is set to fluorescent and you can easily correct the magenta color cast. Do that with a JPEG and your image will be hosed.

Your white balance is very wrong. Shoot RAW, for one shot put a white object (piece of paper or something) in the photo, and you will be able to get the color right easily.