Have you tried it from an actual iPAD? A bit of a search suggests that you should be able to check whether the string “iPad” appears in the HTTP_USER_AGENT string, and if that site isn’t providing, it suggests a problem with the site, unless a real iPAD does the same thing (the solution I found in a search was dated 2010, so maybe it’s out of date).
It’s weird that those two agent strings are identical if one is supposed to be emulating something else. What user-agent string do you get if you choose something entirely different?
There should be a mode in your web browser that allows you to resize your screen to certain size. Both Firefox and Chrome have this feature and they also have different sizes for different devices that are listed.