I know that it will save associations when autosave: true
as per https://api.rubyonrails.org/classes/ActiveRecord/AutosaveAssociation.html
Unfortunately there are no such thing like associations_to_save. However there are some rules saying what is being saved when. You can find those here: http://guides.rubyonrails.org/association_basics.html. Points: 4.1.5 (belongs_to), 4.2.5 (has_one), 4.3.4 (has_many) and 4.4.4 (habtm).
UPDATE:
In case of has_many association, the child is saved on saving the parent if child.new_record? returns true (child was not yet saved to db), or the foreign_key column needs to be updated. This is why: