@its_Jan - I’m very glad you found a solution.
Just for reference, I’m circling back with you to let you know I tested this over the last 3 days and my tests had the expected results – meaning the rule ran just after midnight and told me the task was 1 day overdue.
So, unless you had a Due Time on your tasks, I’m not sure what the issue may have been. I’m glad you have a workaround that’s working.
If you decide to pursue a fix, it might be helpful to get in touch with support.