How does multiple creatures sharing a turn interact with once-per-turn abilities?

This question was brought to mind upon reading one of the bullet points in this answer (regarding a Marilith’s ability to take a reaction every turn), which reads:

  • This limits you to one attack per group for certain implementations of group initiative, as well as for groups of summoned monsters that share a turn

This is noticeable in many of the "Conjure …" spells which share this common line (emphasis mine):

The summoned creatures are friendly to you and your companions. Roll initiative for the summoned creatures as a group, which has its own turns.

The language reads "a group…has its own turns", not "the summoned creatures…have their own turns", which lends to the idea that the summoned creatures are not just sharing an initiative, but actually sharing the turn. This Q&A brings up other cases as well, so it does not seem out of the ordinary that multiple creatures could share a turn. My question is: how does that interact with once-per-turn abilities such as the Marilith in the question referenced above, the Cavalier Fighter’s Vigilant Defender, or monsters’ legendary actions.