This is a common issue when dealing with BYOD and mobile devices. iPhone/iPads have always been able (caveat below) to correctly respond to calendar requests and the communications are relayed properly to exchange in our organization so this would appear at face value to possibly be watch related.
That being said, although not enforced Microsoft very clearly outlines in its recommended best practices that no actions should be taken with calendar items from mobile devices. All actions for accepting/rejecting/etc. should be taken from a full Outlook client (I suspect they may have changed that with the Outlook app... and of course OWA has always been ok). Mobile devices should just be for keeping up with your schedule not altering it (I know, I know, defeats the purpose of the devices, I am not arguing that point only mentioning the recommendation).
When using iPhone/iPad you can often take meeting actions without issue... and then occasionally the meeting is only seen on your mobile device and not in your Outlook calendar. Add to it the complexity of delegates and managed calendars and you are very likely going to be missing meetings when using your mobile device for meeting managament.
As for trying to determine if a meeting was accepted from a specific type of device, I am not sure the meeting itself will let you do that. Your best bet will likely be enabling ActiveSync logging at the Exchange level which may let you gather that information - but of course logging will have to be enabled before the acceptance comes in (and this type of logging is very noisy, not something you will want to leave on all the time).