Well that’s probably not a great sign.
To add to Vetteguy’s response, though, this is definitely not reproduction (for sexual reproduction, most starfish pop up onto their “tiptoes” and release the eggs/sperm; for asexual reproduction, they are fissiparous, meaning that they literally split into pieces - typically by dropping a leg or by basically splitting in half - and the split pieces regrow into full stars).
I’m not entirely sure what this issue is, but I’ve heard of one Linckia star that may have had this problem (the link is super old and the photo no longer shows) and recovered from it over a couple of weeks (which is actually not a bad survival rate, based on the low number of cases I’ve seen with this issue).
I’ve seen people speculate that this is just the star everting it’s stomach to eat - it is almost certainly not. There are enough photos and videos of starfish eating with their everted stomachs these days to pretty well rule that out. I’ve seen one person claim this is the star spitting out damaged tube feet and that they do this often in the wild - I can find exactly zero evidence to support that claim, and I find it rather dubious (if anyone has evidence of this, I would be very curious to see it).
My unprofessional guess is that this is some sort of intense stress response or a bacterial infection of some kind (probably resulting from stress and/or less than ideal food/water conditions). Interestingly, most of the cases that I’ve seen that I can recall this with have happened similarly to your own (meaning this issue started about 2-3 weeks after they purchased the stars and added them to their tanks).
It’s possible it’s something with your tank parameters/conditions (such as high organic nutrients that, to my understanding, don’t read on most hobbyist tests), or something happened during the acclimation process, or even that the star was having unseen issues before you got it/the issues may have been caused by issues that occurred before you got it. I’m not sure.
From what I’ve seen, normally when stars die in aquaria they start dropping limbs and disintegrating (it kind of looks like they’re turning to ash). This looks different to me.
I’d say follow the fish disease forum guidelines and post your tank info and water parameters and see if the collective here can find anything off, but starfish sickness is not a very well understood field just yet.