To generate a visit on AT Internet's side, the redirection from an external source must be correctly completed and the destination page must be fully loaded by the user. The campaign tag must also be present in the destination URL.
What's more, if a user clicks twice on a Facebook link (due to connectivity issues on their end for example), this counts as two clicks for Facebook but only one visit to your site.
A visit is a set of pages visited within a delimited timeframe.
Example: A user consults their Facebook feed, clicks on your tagged link, accesses the page on your site. They then go back to their feed and click another tagged link of yours. If 30 minutes (by default) have not passed between the two events, only one visit will be counted for 2 clicks.