OK I got it to work, but I'm not quite happy yet. After uninstalling the Anixis PPE client, the password reset link appears as it should. Following the link, the PPE rules are displayed correctly in the web interface, so that's fine as well. BUT when users just want to change their password from inside their Windows session, I am now missing the little window showing them those rules, something the Anixis client provided.
Is there some way to get both to work? Maybe change the priority of those credential providers, with the Adaxes one being first, so that, even though the Anixis client is installed, the password reset link still appears? Sorry if I'm just guessing, this goes a little bit beyond what I normally do.