Hmm, the output base view from your RP file is correctly loading on our iPhones and various mobile devices, all under 533 pixels wide. Would you mind sharing the exact Axure Share URL you're using? Were there any changes made since your last project upload? It looks as if the prototype associated with this RP is password protected. Testing the exact URL may be a good next step.
Next, I'd want to make sure that the output sitemap is fully closed out when you're viewing, instead of simply minimized. From the RP 7 output, tapping the "x" icon in the sitemap would be needed as opposed to tapping the minus (-) symbol.
In addition, can you post a screenshot that shows what you're seeing on your mobile browser? It sounds as if the rendering is inconsistent, sometimes showing the 533 view and other times showing the 960 view. Are you able to reproduce these in a consistent way?
Let me know what you find!