Now getting to the question about what you are doing.
Lips: Do not curl, roll, or clamp. The shape change involves the aperture corners, the jaw, and the tongue.
Practice the concert hall breath and then say aah-ooh – that’s your embouchure. Practice this over and over and again. Release your air into a strip of tissue as demonstrated using the “tu” syllable.
It is important that you practice this often and then practice the leadpipe. When you play C on the trumpet, you should have a good or great sound. Play C# and F# without slurring and each note should sound good. Copy Greg’s sound.
Playing lower notes and higher notes by pivoting the horn is something you should NOT be doing. Any pivot that happens is very minor and would barely be noticeable. You should not consciously shift the horn’s angle or position to play C# to F#. (Maybe Greg should rerecord that demonstration. It could be because the volume air and an exaggerated change in his tongue and jaw position are causing his horn to pivot up and down.) Step 4 is a better demonstration of what you should be doing. Learn slurring from C# to F# by a change in aperture corners with a slight change of the tongue and jaw. The back of the tongue will rise a little and the jaw may close a little when changing to F#. The tongue/jaw lowers when playing C#. Any motion of the horn is very slight as the shape changes.