I see. I suppose just experiencing that parent is "out there" and will come periodically to check on them might make the infants feel calmer. It definitely seems better than just leaving the child to cry the whole night.
Extinction actually has a specific meaning in behaviourism, it refers to extinguishing an unwanted behaviour (signalling at night) rather than wanting to extinguish the baby - it's a term used in behaviourism and can be applied to any unwanted behaviour, not just crying at night.
The connotations of using that term are rather unfortunate but there's a reason why that name is used.