The FITS viewer shows you what it thinks is the correct color via a quick linear stretch. Depending on how it does the stretch, the preview will differ from one FITS viewer to another. I wouldn't judge color representation from a FITS preview. More mature processing tools have photometric color calibration capabilities to help as part of the processing workflow.
But given your image is in dual narrowband, your filter captures Ha and Oiii, and your target is Ha rich, red color is not far fetched result.
In post-processing you can adjust the color as you see fit. Some split the Ha and Oiii channels and process separately to taste. Everyone to their own
