The button isn't a feature to be turned on or off, or to work/not work for specific browsers. All it is, is a link to the #top of this page, right within the html code itself. here's the link that the browser interprets when you press top:
Code:
https://www.ninjette.org/forums/showthread.php?t=292688#top
Even the Next Thread buttons are (very) slightly more complex, in that it is pulling up a function within the showthread php file.
Code:
https://www.ninjette.org/forums/showthread.php?t=292688&goto=nextnewest
If the "top" button isn't working, it really can only be that your browser doesn't see where the #top is in the code for the page that you are currently on. It is in the html code (just look at "view source", so if it isn't recognizing it, it has to be something like a cache issue or other browser glitch.
On your iphone, which browser do you use? Whether it is Safari, Chrome, or other, try another one to confirm it's just a single browser problem. Figure out how to clear cache/remove internet history for whichever browser is giving you trouble. Go to App Store, hit Update in the bottom right, and make sure every app is fully updated.