Reminders app on desktop

I agree, that wasn't put nicely. I saw some warning too, but I didn't really understand what it meant-- I knew that my MacBook Pro JUST upgraded somethingrather, and I didn't keep track of the exact release number. Now I'm out of luck for awhile.

In the meantime, we'll have to go to the https://www.icloud.com/reminders/ on our notebook computers. Not that bad.

Any idea when this problem will be fixed?

You will have to wait until Apple releases macOS Catalina. If you read carefully the "warning" that you got when you enabled the new Reminder app on your iPhone, you would have seen this.