If the project that contains an action is due, the action is treated as if it has that same due date, whether it has no explicitly assigned due date, or a later one. It sounds like some of your projects have due dates that you don't expect.
I would go into iTunes with iPad connected, select the Apps tab, go to the bottom, select OmniFocus, click on the OmniFocus.ofocus file on the right and save it to the desktop. The support ninjas may be able to figure out what happened from the transaction history contained therein. Do that before you do anything else, to avoid obscuring any evidence. Then send them a report at
omnifocus-ipad@omnigroup.com and attach the file.
As you also have the Mac application, you can open up view showing projects sorted by last changed to see what/when changes were made to your database to add the spurious due dates, and do similarly in a context mode view to see if actions were changed.
Have to say this is an odd one, on the face of it!