First, note that the setting in Due > Settings > Editor > Default Snooze affects only newly created reminders, and not the auto snooze setting of existing reminders.
To modify the auto snooze of existing reminders, or to set a different auto snooze for a reminder, tap on a reminder to bring up the editor.
Then, tap on the auto snooze button on the top (2nd button from the left), then choose the auto snooze value that you'd like for that reminder.
If your setting is correct but your reminders are still not respecting the auto snooze setting, look at the Troubleshooting steps below.
If your auto snooze setting for the reminder is correctly set to Every 5 / 10 / 15 / 30 minutes, but you're receiving alerts every minute instead, you could be missing a receipt. Try setting the reminder to the auto snooze of your choice again following the steps above, and you should be presented with the Unlock new features screen.
Follow the steps in the article Already Paid For Upgrade, But Asked To Unlock Again to restore your purchase and functionality of Every 5 / 10 / 15 / 30 minutes snooze.