No, it's not ambiguous. It's an idiom, and it has exactly the sense that you said was "pretty clear".
The thing is, stop only takes gerund complement clauses, and does not take infinitives.
- Stop hitting it!
- Have you stopped beating your dog?
When an infinitive clause occurs after stop -- in exactly the place it would if it were a complement (thank you very much, English syntax) -- it is not a complement (i.e, it's not what you're supposed to stop doing). Rather, it's a purpose infinitive (i.e, it's an adverbial clause explaining the purpose of your stopping).
You can tell the difference if you substitute an adverbial phrase for the infinitive.
- He stopped to hit the dog
- He stopped ((doing something), in order) to hit the dog.
The idiom I mentioned in the first line is the once NP VP construction, as in
- I understood it once he showed me how it works.
- Once you eat durian, you'll see what all the fuss is about.
The VP has to be an event; pure stative predicates are interpreted as change-of-state events, which are called Inchoatives /ɪn'kowətɪvz/ in the trade; it's a great word to throw into a cocktail party conversation.
- Once she was tired, she took a rest.
- Once I own that house, I'll gut it.
- Once he's tall, he'll sink it every time he shoots.
... and, like all idioms, it sounds very weird after you repeat it a lot. Welcome to syntax.