Yeah, this was part of the confusion TBH. It even has the same question with devā generally. It seems whenever the Buddha was asked this question it got complicated somehow 
It seems that in the MN 90 passage, the king may be asking the Buddha essentially what Gabriel said quoted above in OP: Do the gods self-exist, or do they exist conditionally and are reborn like other people. In other words, ‘absolutely exist’ here could be what is meant. He rephrases this by asking if the gods are reborn or not, and the Buddha responds by describing the causes that would cause this to be the case: if they have afflictions yes, if no, no. So here we see cross over again: there is a distinction between some causal aspect of the gods’ existence and their existence in another sense.
Maybe the Buddha had already experienced the question in MN 90 and others like it. So when someone asked him the same question at MN 100, he automatically responda with “I understand about the gods in terms of causes.” This is all fine and good; the problem then becomes that he says that anyone would come to the conclusion that the gods do ‘atthi’ from what he said. So on the one hand he’s avoiding the word ‘atthi,’ but on the other he just gives in and says it. This would mean that at this part of MN 100 it cannot mean ‘self-exist’ or ‘absolutely exist.’
The other way of reading it in light of MN 90 is if ‘atthi’ does mean ‘survive’ or ‘will exist’ after death in the sense that ‘atthikavāda’ refers to rebirth and non-annihilation, etc. He does not immediately say ‘yes’ because it is conditional: some do and some don’t depending on their afflictions. In other words, he would automatically assume ‘atthi’ to mean what the king clarified in MN 90: “whether or not the gods [are reborn].” He then clarifies that someone would realize that yes, they are reborn — he was just making clear the nuance here. This all hinges on a different reading of ‘atthi.’
It all boils down to that at the end, it seems: what does atthi mean here?, and how does it relate to the meaning at MN 90? I also think it boils down to what people thought of the gods.
On Bhikkhu Bodhi’s notes to MN 90 he says: “K.R. Norman, in an interesting paper, has proposed a radical re-editing of this portion of the sutta, which would entail important differences in translation, but as his proposals are not supported by any editions I hesitate to follow him. See Norman, Collected Papers, 2:162-71.” Anyone know about this? Looks like he has a paper called Devas and Adhidevas in Buddhism [JPTS] and another ‘The Buddha’s View on Devas.’
EDIT: I’ve found more info from Piya Tan. We have a summary from Norman on MN 100:
[t]he circumstances in which the brāhmaa Saṅgārava asks the Buddha about the existence of devas are not clear in the PTS edition of the sutta, for the details are omitted there and readers are merely referred back to a parallel passage in another sutta. In fact the question is asked immediately after the Buddha’s statement that devatās had approached him and shown him great concern about his weak condition during his pre-enlightenment ascetic stage. The purpose of Saṅgārava’s question can only be to ascertain the Buddha’s view on the eternal reality of devas, since the story he had told about the devatās necessarily implies that he admitted some sort of existence for them.
(Norman, “The Buddha’s view of devas,” 1977:331)
After some philological discussion you can read in the article, Norman comes to this conclusion:
I suggest therefore, that the text of the sutta should be corrected by changing atthi devā to atthi adhidevā in the three sentences (B), (C) and (E). It will be seen that the passage is then no longer puzzling. The Buddha is asked, “Do devas exist?” He replies, “I know for a fact that adhi- devas exist.” Saṅgārava’s anger is understandable. Is the answer not off the point? The Buddha replies, “If anyone is asked if devas exist, and replies that super-devas exist, then anyone with sense can deduce that devas must exist (for super-devas are superior to them). Saṅgārava then asks why the Buddha did not say in the first place that devas exist. The Buddha answers that (it was unnecessary because) it is firmly accepted in the world that devas exist. Saṅgārava is satisfied with this reply.
However:
Analayo, in his comparative study of the Majjhima Nikāya, however, finds that the Madhyama Āgama as preserved in the Chinese translations does not support Norman’s reconstructions of the Kaaka-t,thala and the Saṅgārava Suttas.
Apparently, in the Sanskrit parallel the question on gods comes first before the Buddha describes his process of awakening and realizing things for himself. Analayo argues that this is the most sensible arrangement.
Gonna look into it some. Here’s Piya Tan’s paper: link here
I think that the point that these people must be asking about the eternality of the gods is the most relevant, and I think it must be so. Sangārava was a learned brahmin who performed sacrifice, and King Pasanedi also sponsored sacrifices and was a student of the Buddha/srāmanas as well. As MN 100 says, the existence of gods was widely accepted; it was a small minority seemingly who denied it and it seems obvious that the Buddha believed there to be gods and that these two men did as well. This is perhaps why the Buddha asks what King Pasanedi means at MN 90, to which he responds that he’s asking about their rebirth or not—not their plain existence. MN 100 is less certain, but if we understand atthi not as meaning an absolute eternal ontology but merely temporal continuation (the same context as those in which views of ‘atthi’ mean views of rebirth and post-mortem survival in the suttas), then this may be the reading. Still, a conventional ‘there are gods’ feels more natural for the interaction at MN 100. 
Mettā
Thanks. Yeah, this is how I see it potentially being as well. I’m not sure if he was thinking of the tetralemma specifically, but that’s an interesting point and it very well could be so. I suppose it is somewhat implicit in “I understand gods in terms of arising/ceasing conditionally.”