Just to get on the same page here - you already replaced the alternator and nothing changed, the water pump is still running? I would check the voltage. Use this article here for help:
BMW E90 Alternator Replacement | E91, E92, E93 | Pelican Parts DIY Maintenance Article.
What rebuilt alternator did you purchase? Did you purchase it from us? If the alternator tests out well it could ultimately be a faulty water pump. I have seen this before when individuals have replaced the alternator, even with a new recently installing a water pump. Yours should still be under warranty if it turns out to be the problem. Let me know what you find out.