iPhone alerts from unchecked calendar

My wife and I use the same Apple Id but use different calendars for our events. After I got my Apple Watch, I did not want to get my wife's alerts, so I disabled her calendar on my iPhone. Her events indeed disappeared from my Calendar app but her alerts nevertheless are active. After talking to Apple and looking at the iCloud.com on my Mac for two hours I had the problem diagnosed as sharing the Apple ID.

As a software engineer for 46 years, this does not make sense. The problem is obviously Apple's implementation of the iCloud calendars. If I unchecking a Calendar does not remove a calendar's alerts, why bother providing the check?

The Apple advisor also mentioned separate iCloud accounts. I thought each Apple ID has one iCloud account. Is that not true? Why have two separate iCloud accounts vs separate Apple IDs? Is it difficult to separate a shared Apple ID and still keep the same apps and other settings?

Any ideas or suggestions?