Key Concept
Despite testing with responsive simulators and ensuring there were no issues, some iPhone users have reported problems with the style of my web page.
Coding Essentials
The page is designed to use 2 custom CSS files - one for screens larger than 960px and another for smaller screens (<=960px).
One important meta tag used on the page is:
<meta name="viewport" content="width=device-width, initial-scale=1">
Here is the page I am testing.
Testing and Outcome
Testing on various browsers resulted in no issues with small screen sizes down to 260px width. The CSS has also been validated here.
However, some users have reported display issues specifically on new iPhone 6 browsers (both Safari and Chrome show the same problem). This issue does not seem to affect other phone models.