A gentleman from Fujifilm Germany kindly replied to my request (I summarize):
"The pink stain in Provia is most likely anti-halation and other dyes not properly washed out. It is a rather "cosmetic" issue, as the stain should not show up in projection and does not affect long term stability of the slide. The pink stain is linked to the 3-bath process, Fuji thus recommends the 6-bath process. The 3-bath process should be completed with extra washing and an extended soak in a dilute sulfite solution, prior to the final stabiliser."
This info is fully compatible with Rudeofus' note above.
I have soaked some pinkish filmstrips for 20 minutes in ~35°C warm water (one change after 10') with 1 level teaspoon Na-sulfite per litre, then STAB again: The stain is gone.