If you use the diminished 7th arpeggio on a diminished chord, like A dim7 arpeggio over an Adim7 chord for instance - then we start on the root of the chord (and then play the arpeggio - minor thirds on top of each other) to get the right notes and right sound over that chords. (Notes: A, C, Eb, Gb)

What I talk about a lot in this video though, is the use of the diminished 7th arpeggio over dominant 7th chords. We use that to create tension, leading to the next chord.
So if we play the diminished 7th arpeggio over a dominant chord (A7 for instance), we start on the flat9 (which is the 2nd note or the scale if you of the chord and then play the diminished arpeggio.) Because otherwise we don’t get the right notes over that chord. You can also start the arpeggio on the 3rd (C#), or the 5th (E) or the b7 (G) or the b9 (Bb) like I mentioned above.
We are treating that A7 chord as a A7(b9). That’s why we don’t start the arpeggio on the root of the A chord. Cause then we’d get the notes A, C, Eb and Gb and that won’t work over A7(b9).

Hope this makes sense! Let me know if you have any more questions!
Kind regards /E