Run function when WordPress new multisite is created or ACF field is updated

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Create a plugin for the mu-plugins directory and have your function run when the wpmu_new_blog action fires.

Reference, here: https://codex.wordpress.org/Plugin_API/Action_Reference/wpmu_new_blog

The hook you cited for ACF seems to be the way you ought to run you function, if you want that to happen upon ACF save…