As you've rightfully pointed out, s.t() is to track Pageviews. Whereas s.tl() is normally used to track Custom Links, but can also be used to track Exit and Download Links.
With both calls, you can include any props, eVars and events that you want (and that make sense to be tracked together).
But also like what @evolytics_brian said, it looks like you actually have another problem, which is that your click on what should be an internal link is being tracked as an exit link because of incorrect Internal URL Filter setup.