It should be noted that the Safari browser, which is widely used on iOS, refuses by default to accept third-party cookies.
In this case, the SmartTag file uses the value of the cookieDomain parameter to automatically set a first party cookie instead of the traditional third party cookie. The value of this parameter must correspond to the domain of the site in order to allow the deposit of first party cookies.
It is possible to modify this parameter via Tag Composer (in case of modification, do not forget to re-download/re-deploy the new version of your SmartTag file).
It is also possible to force the right domain when initializing the tracker, as follows:
var tag = new window.ATInternet.Tracker.Tag({'cookieDomain':'.my_domain_name.com'});