"if someone works on a song that ends up on an album, will they get royalties etc. from the sale of the physical album? even if it's just a tiny cut?"
this completely depends on the contract the songwriters/artists have with the publishing company i.e. label. one can write and produce a song for an artist and either get paid solely as a flat fee (more common when the artist is unknown so you negotiate a higher upfront fee because you don't think the royalties will be much), solely on royalties (I think this is rare, but an unknown producer might offer it as an incentive - sort of a no-win no-fee situation) or as a mix of both (this is most common. a standard percentage is 10-25% for the producers).
same for someone who performs on another artist's song: a session musician or backup singer is more likely to get a flat rate, a feature artist might get a cut of profits (royalties), or it might be a swap deal where they don't get why payment but the other artist promises to feature on a future song of theirs.
there is no way to know for sure unless the parties involved divulge that information, as it is confidential business info.
in this case that we're all thinking of right now, it's most likely that the external producers will get royalties as well as an upfront payment, but we'll never know unless they tell us.