Hi,
I'd just like to add a comment.
In this example, ate out of their hands has a literal meaning. However, unless you have a pet fish that you feed like this, usually when you encounter these words, they will not be used literally.
eg The boss is eating out of Tom's hand means that the boss believes that all Tom's ideas are great, that Tom is a wonderful guy, the boss will do anything Tom wants.
Best wishes, Clive