If you decline the upgrade Reminders will work as it has, on all devices. I did so with iPhone X and iPad Mini 5 on Public Beta, with a MacBook Air mid-2011.
Functionality is “limited” to what’s currently available with 12.4 and current/older versions of Mac OS.
Right guys, I've been doing a bit of testing and here are the results.
Right now my Reminders screen looks like the screen below. The List blacked out is my .mac / iCloud list. I haven't yet Upgraded My Lists, so does that mean that the app I see below is the old Reminders app? What would happen if i DID Upgrade My Lists? Is this the thing that will prevent reminders syncing across to older iOS and El Capitan?
The tests I done were:
* I added a reminder on iOS 13 (iPad). This reminder synced across to my iPhone running iOS 12 and Mac OS El Capitan.
* Added a reminder on MacOS El Capitan. This synced again to both iOS 12 & 13.
* Added a reminder on iOS 12 & 13 .mac List. These synced to all devices.
So, so far all is working as normal. Therefore, I'm very tempted to upgrade my daily iPhone to iOS 13.
But the BIG question is, what would happen if I were to hit the Blue 'Upgrade' button next to lists?
PS How frustrating is it that there is not + button at the top of the screen to add new reminders! You have to scroll down to the bottom of 'Today' to see the + option.