Hi @gwion and welcome to the forum,
I can’t help you with the first part of your post - I’ve not used Airtable - but for the second part, yes, by default it will fire for any changes, but you can specify a filter to limit it to only certain types of changes.
See “Filtering” here:
https://developers.asana.com/docs/webhooks
and I’d also recommend searching the Developers & API forum section for “webhook filter” as there are some discussions of it here, also.