That's intriguing. I use the regular (non-Exchange) versions of Appigo Todo on my iPhone, iPad, Mac and the web and all devices sync happily using the same account credentials. I'd be surprised if this wasn't the same for the Exchange version but I guess anything is possible.
Appigo Support should be able to help. You can log a ticket with their website or use their Facebook page - they're generally fairly prompt at responding. Good luck.