As I understand it ...
'tagging' means that the "URL" (link to a person's profile) has been placed within the text of a discussion message.
There are (generally) three different ways that 'tagging' can happen:
(1) Copy and paste that URL into the text (more on this below).
(2) Type an "@" followed by the first few characters of the person's name. That should 'pop up' a list of names to choose from.
(3) Start a Discussion from the "Discussions" tab of that profile. This tab is not available for claimed profiles or private profiles you don't have access to. And, of course, it only applies to 'tag' that one profile!
Method #2 depends on the "caching" of profiles which you have "visited" (viewed) recently or are "near you" (in your family group). It is not always reliable. This is often known as a 'short-cut' for tagging.
One can get to the "URL" (for use in method #1) in a variety of ways, depending on what is "visible" at the time. When a person's name is visible as a 'hot-link' on the page (often in blue), then a 'right-click' or 'control-click' on that name should bring up a small contextual menu of options -- one of those options should be "Copy Link Location" or something semantically similar. Selecting that item will then 'copy' the URL.
When pasted in the text, it will initially look something like:
http: / / www . geni . com / people / persons-name / some-long-number
(without all the spaces, which were put in so it does NOT become a link!) If the text does not contain the "PEOPLE" in the path, you didn't get the correct URL! It is that "URL" which 'tags' the person.