Another way to fix this without disabling Exchange reminders is to change the iPhone default calendar to a calendar other than the Exchange calendar. E.g. your iCloud calendar.
This also allows you to use location-based Reminders again, because new Reminders get created in the iCloud calendar instead of the Exchange calendar.
This does however mean that any new Calendar item (meeting etc.) created on the phone will by default be created in the iCloud calendar too unless you manually pick your Exchange calendar when creating a new Calendar item.
Some may find this annoying and prefer to stick to the simple solution of switching off Reminders. Note that this still means that all new reminders will be created locally on the iphone, or on icloud if you have an icloud account set up. Reminders will never show up for example in MS Outlook any more. The way around this would be to install Apple's iCloud application on your desktop and choose to display iCloud reminders in Outlook. This way you would then see your iCloud reminders from your iPhone in Outlook again! Phew.. what a workaround 🙂