Starting with Sytist version 1.2 is the option to have custom favicons / icons for each gallery. This is shown in the browser tab, when bookmarked and when added to the home screen of a tablet or phone. This can be enabled in Settings -> Photo Settings.
The photo it creates the icon with is the preview / cover photo and is done automatically when photos are uploaded to the gallery or if you select a new preview photo from existing photos or uploaded a different preview photo.. So it is the first photo in the gallery unless you select a photo to be the preview photo or upload a custom preview photo.
If you are updating to version 1.2, it won't automatically create these for existing galleries. You would have to view the photos in the gallery in the admin to have them create (just viewing the photos page will create it).