Hi, I was one of the authors of this! I think we briefly mentioned this in a footnote somewhere (a lot of things got cut or moved to footnotes since it is already so long & wanted to focus on the ML parts that aren't described elsewhere).
But yes as @Flobosg mentioned, for protein chains they use jackhmmer to search 4 of the databases (except when searching Uniclust30 + BFD when HHBlits is used instead) and for RNA chains they used nhmmer to search then hmmalign to re-align these to the query chain.