I guess for test on iOS would be to see if you could store something to localStorage as that doesn't work in safari would be one way to tell of your in incognito mode.
It would be nice if there were an app like CookieAutoDelete [0] for mobile Safari (or desktop Safari if Mozilla keep misbehaving!). You can disable cookies but that's trivially detectable. I guess it's trivial to detect, but it needn't be; something akin to Mozilla's Containers [1] on mobile Safari would be a step in the right direction.
[0] - https://addons.mozilla.org/en-US/firefox/addon/cookie-autode...
[1] - https://addons.mozilla.org/en-US/firefox/addon/multi-account...