You're supposed to photoshop your sample images before you send them off to the customer.
Seriously, it all comes down to color gamma. The CCD in the camera can do a pretty excellent job with color gamma these days, but for some reason the camera chip is picking up something on your refinished sample and during the conversion from RAW to your chosen colorspace it's not blending the colors the way your eye does.
And, by the way, what is the color temperature of your fluorescent lights?
https://www.gtilite.com/2015/08/the-five-keys-to-accurate-color-viewing/