AT Internet sets different cookies on users' browsers via the tags, depending on the way they are implemented.
You can check the lifetime of cookies in xtcore.js' source code by looking at the xt3 (lifetime of the main cookie, i.e. Unique Visitors) and xt4 (campaign persistence cookies) variables' values.
You can also access the information via the browser; check all the cookies deposited on your domain and ours (xiti.com) to know their lifetime. On most browsers this can be achieved by clicking the information icon to the left of the URL.