Is the garden open only when the museum is open, or is it open all the time?

Yes, you are correct. There are times when all the gates will be closed.

My impression is that ALL the related museums are "open" with regard to their gardens and outside displays. Hint: go to the Rodin first; entrance is a contribution (not a set admission fee) AND your receipt is a deduction at the main art museum. [Our visit was on a downpour day, so we didn't spend time in the gardens.]