In WiNLY Ingo says he's not very religious. What that means in (my version of) the Pokéverse is that he knows that gods do exist, there's very little room for debate there*, but he doesn't believe that they involve themselves in human affairs, but just off somewhere doing their own thing. He still uses 'Dragons' as an expletive, even without his memories, because that's more of a cultural thing than a religion thing, but he uses the word as just an intensity modifier and doesn't attribute any additional meaning to it.
(*There would be a small subset of people who actually do think legendaries are just really strong Pokémon and not gods, but they'd be a small minority.)
Emmet on the other hand does believe the Dragons play some role in people's lives, namely their own. Emmet explicitly thinks their fusion ability came from the Dragons. This is mostly because he's the sort of person who wants an explanation for everything, but since Ingo is uncomfortable with the fusion ability being studied in any scientific way, so he decided the Dragons were the explanation. And (although this isn't really showcased in WiNLY) Emmet is more likely to invoke Reshiram or Zekrom specifically depending on the situation.
Ingo really latched onto the Pearl Clan's capital-s Space thing because it fit in well with how he perceives/interacts with the world. But again, he considers it a culture thing, not a religion thing. Emmet just absorbed it directly from Ingo.
Emmet's time thing is more to do with routine than actual time itself, so Time doesn't get the same treatment despite them having spent much more time with Melli than with any Pearl Clan person.
Legendaries in WiNLY use capital They/Them specifically because, when I write 'they', I wanted it to unambiguously refer to Ingo and Emmet as often as possible. That's also why Lord Electrode, Mignon, and Magnezone all use it/its, though I really wanted to use they/them for Electrode at least.