I am building an app (iOS) which consists of paged tiles which the user has to pan through.
My question: When I need to tell the user to move the content up to view the content below it, should I say swipe up or swipe down?
You should use neither of them. When you are referring to vertical content, you should say "scroll up" or "scroll down".
Vertical content movement has been used for decades now, and there is no good reason to change the terminology. Yes, you are swiping, but you shouldn't refer to how it is done, just what you want to achieve.
We say "click on X" not "move your mouse so that the cursor moves to X and then click your mouse button". How something is done can change, but what you want done should as much as possible be independent of the technology being used.
Yes. Apple use the terms "swipe up and swipe down:
The Apple HCI Guidelines may be of use here in conveying defined actions:
On avoiding redefining gestures: https://developer.apple.com/library/ios/#documentation/UserExperience/Conceptual/MobileHIG/UEBestPractices/UEBestPractices.html#//apple_ref/doc/uid/TP40006556-CH20-SW22
Apps respond to gestures not clicks: https://developer.apple.com/library/ios/#documentation/UserExperience/Conceptual/MobileHIG/Characteristics/Characteristics.html#//apple_ref/doc/uid/TP40006556-CH7-SW4