Yes, that passage is from 'The Istari' in
Unfinished Tales, and appears in the notes after the main essay. It is not clear to me (or to Christopher Tolkien, apparently) whether this chart is meant to show which Vala each of the Istari was attached to, or rather, which of the Valar spoke up for them and chose them in the council he had just described. In that Council, Manwë is the one who chooses Olórin to go, after Curumo and Alatar have been put forward, and Varda comments 'Not the Third,' suggesting that she has chosen him as the leader of the Istari. So, certainly, we want Manwë to send Olórin in TA 1000, which is why it is so important that Manwë see Olórin as an emissary now. It is less clear to me that he need be one of Manwë's people.
Here is what the published Silmarillion says about Olórin (leaving aside 'Of the Rings of Power and the Third Age):
Wisest of the Maiar was Olórin. He too [ie, like Melian] dwelt in Lorien, but his ways took him often to the house of Nienna, and of her he learned pity and patience. Of Melian much is told in the Quenta Silmarillion. But of Olórin that tale does not speak; for though he loved the Elves, he walked among them unseen, or in form as one of them, and they did not know whence came the fair visions or the promptings of wisdom that he put into their hearts. In later days he was the friend of all the Children of Ilúvatar, and took pity on their sorrows; and those who listened to him awoke from despair and put away the imaginations of darkness.
I agree that dwelling in Lorien does not necessarily mean that a Maia is of the people of Irmo or Estë, though that would seem likely. Frodo did see Gandalf imprisoned at Orthanc in a dream, so it is possible to make some tenuous connection between Gandalf and dreams, if you wanted to, but I think that Frodo's 'meaningful' dreams are not connected to Gandalf and it's not necessary to go that route. More significantly, we would have had no reason to see Olórin on screen before this episode, and thus it seems unlikely that Manwë would know him (especially if he's been living in Lorien, which was just introduced at the end of the previous episode). Conversely, if he's been one of Manwë's people all along, it seems unlikely that Irmo would know who he is (and we wanted Fëanturi in this episode).
But I (in general) am in favor of erring on the side of permitting all interpretations permitted by the text. So, if there is ambiguity in the text, we should at least attempt to preserve that ambiguity and allow others to draw their own conclusions (when possibile - we're going to have to make decisions about whether Orodreth is Finrod's brother or his nephew, and the lineage of Gil-galad cannot be left up in the air). So I will definitely make that change where Irmo suggests him, but does not 'claim' him.