We have a situation where a user (Who use to be a System Administrator, but is n

How many Gateways are you running on?

Our solution is cloud based.

It has been observed that at time user profile changes do not propagate to all Gateways. In such cases updating user profile again may help. In case it does not, you can check with cloud team and ask them to verify if all Gateways are in sync.

What version are you on? Did you recently have any upgrades?

7.11 and no upgrades recently.

@benjamin- As per my knowledge when a user is created with role of system administrator, it is added to various groups like Process administrator, designers, etc.
Now when you change the user role to basic user Appian does not remove that user from those groups and hence user can perform actions or receive alerts. When you change user role make sure you remove that user from above mentioned groups. I hope this will resolve your issue.

User in question is not a member of those groups.

Is there any process model published by this user? If yes, try to republish them by another user.

No

Then you will have to investigate one of the affected process models. Check security roles. Check all groups related to this model. It could be that a process inherits its security settings to a sub process. Not sure if this inherits the models admin role as well. Are the notifications sent by processes running since before the user switched role only or also by processes started just recently?