The linked paper describes the reaction in conditions similar to that you describe. It appears to be likely that fluoxetine would react with hypochlor which is that is generally understood to be that was added if water is described as chlorinated.
I performed experiments with spiking water with pharmaceuticals in Zurich about 15 years ago and the tap water contained much lower concentration of chlorine in the order of 0.2 ppm and I believe I remember it was chloramine. If your water contain chloramine the conclusion would be different as chloramines is much less reactive to organic amines.
Article Reactions of the amine-containing drugs fluoxetine and metop...
Thank you very much for your answer and for this paper, indeed very interesting and helpful. I will find out what they use to chlorinate the water in our facility.