Akvan said: “So tadassādeti, taṃ nikāmeti, tena ca vittiṃ āpajjati. Tattha ṭhito tadadhimutto tabbahulavihārī aparihīno kālaṃ kurumāno brahmakāyikānaṃ devānaṃ sahabyataṃ upapajjati.“
This is part of the quote that I gave from the sutta in my response. I have highlighted that and its translation there too. That means “He savors that, longs for that, finds satisfaction through that. Staying there—fixed on that, dwelling there often, not losing the jhana—then when he dies he is born with the devas of Brahma’s retinue.”
You also said, “All explanations of first jhana (ariya or anariya) mention viviccha kamehi, viviccha akusalehi dhammehi, which means abstaining from kama.” That is correct too. It just says one has “withdrawn from sensuality (kāma), withdrawn from akusala”, and leaves it open whether it is just suppression (vikkhambana pahana) or permanent removal (ucceda pahana).
So when you said, “This rebirth in the Brahma realm (for an ariya or anariya) is due to the gathi of the person and not due to a magga pala. yadidaṃ gatiyā upapattiyā sati.”, that is correct. Both are born in that brahma realm.
But in the same verse below that (which I also highlighted in my earlier response) explains what happens to a normal human and an Araiya after that life in the brahma realm comes to an end. The anariya, who had only suppressed kama raga (vikkhambana pahana) to get to the first jhana, comes back and may be born in apayas. But the Ariya (disciple of the Blessed One), who had removed kama raga (ucceda pahana), attains Parinibbana without coming back to kama loka.
So, when you said, “For an ariya, he does not return to this world and therefore could be called an anagami, however it does not necessarily mean that he has attained anagami pala.”, that is NOT correct. It is effectively the same, since he will get the phala moment there and then be reborn in a suddhavasa reserved for Anagamis. Anagami means “na agami” or not coming back to the kama loka. For that, he would have removed (ucceda pahana) kama raga.
This is a grave error made by even some followers of Waharaka Thero in Sri Lanka these days, even though Waharaka Thero has clarified this in his dessnas. The following is such a desna, and of course it is in Sinhala: “Ariya and Anariya Jhana“.
That is why I am emphasizing this. But of course, it is up to each individual to decide for oneself.