Do you notice how the lighting gets brighter and brighter as the shot progresses? I know this has to do with the angle of the light but is there any way to avoid/prevent this or set myself better for this?
You must set Exposure (Iris), Gain, Shutter speeds to MANUAL on the camera, which apparently was on AUTO for that scene. What is happening at start of shot is the bright window is prominent in the frame, so camera compensates and makes overall image darker, then as you pan away from bright window and darker room fills more of frame, camera wants to then expose for that scene and opens things up to let more light into camera.
Manually set exposure for darker part of room before you record, then as you move away from bright window, the rest of the room will be properly exposed without image brightness changing as it did.
Also, if you can't re-shoot and need to fix clip in Premiere, apply color correction and then use KEYFRAMES to alter the color correction over time to hide the dramatic lighting change. I've had to do that before myself! In other words, make image brighter at start, then ramp down that brightness correction to "no change" as panned video moves towards proper exposure.