The lighting is 90% of the issue with colors as the eye can tell.
Sea salt mixes contain iron & all kinds of various minerals and if you use the same salt mix on 10 different tanks yet use different lighting on ea tank the same exact coral will look completely different in ea tank, sometimes wildly different depending on the coral species.
This is easy to test, several sites that sell corals online show you this and its explained so that the buyer wont think something is wrong with the frag when its just different lighting params and corals will adjust their algae in their flesh to end up compatible with the spectrum along with looking different then the purchase pics.
Purple is a good color it means the coral is thriving, in my tank my birdsnest is pink but im running all T-5 HOs no LEDS and ive read that many corals show better color on T-5s unless the setup is really tweaked to match bulbs closely.
Also some Birds nests corals are purple not just pink it differs with species & depth and very possibly lighting but the lighting can be easily determined by asking what lighting was used on said coral that looks pink in pics if they dont state it but most do.
Many reefers run too much blue and less natural light that effects corals after a while also as they need natural bright light, ultra violet, and "violet & some blue" for florescence eye candy for our eyes.
You could probably try dosing iron but to be honest if water changes are done at least monthly iron is added anyway & if no visual change is noticed its not an issue.
What lighting are you using?