Sybe.
If this sutta (and others) say so, then I will not contest the point. (I have just read the relevant part)
However,when you were referring to “then there is still an influence of that mana on the mind of an anagami. I think we can talk about this as mara’s sway, at that moment.” (September 18, 2018 at 4:07 pm),it was about anagamis still in a human body in the human realm, where Mara still has influence over as a location or loka, but not (decisively) over their mindset, which is already that of a brahma.
Thank you for the reference,
Much Metta