Their terminology is odd. The thing you move while playing is generally called the hand slide. There's nearly always a separate tuning slide located in the crook of the bell section.
(Some relatively rare instruments like the Shires Alto do "tuning in slide" with a mechanism for fine adjustment in the hand slide).
If you're also moving the tuning slide in the middle of a piece you're probably a bass trombonist doing the now-impossible glissando (see https://www.youtube.com/watch?v=fWJPeA_1g48) in the Bartok concerto for orchestra.
I was thinking the same thing. The tuning slide is not what you use while playing, it's the separate slide on the bell side of the trombone for fine adjustment to ensure you're in tune with the rest of the band.