After days of testing the problem is with the rules that was created in My Tasks.
My assumption was that the rules times (for example due Today) will be dynamic and will update to reflect the users local time and update if the person moves to a different time zone. After seeing the behavior, I think the rules time is locked to when the rule was created. So, I fixed it by recreating the rules again and now it triggers at the correct time (until I move again).
My biggest concern now is what other rules are affected that I do not know about and does this have an implication when I create rules for the rest of the team and our time zones differ whose “Today” will be used. Not even thinking of what happens when using a VPN.
A possible solution would be to let the user decide to lock it to a specific time zone like I’ve seen on Google calendar where the default is used but one can change the time zone manually.