Definitely NOT legal.
Consider this:
There is no night rating or night qualification in the USA. It does not exist.
Night flying is part of the PPL syllabus and cannot be " added" to anything.
Your US certificate is issued under 61.75 and is a validation based on your JAA PPL and carries all the restrictions of your JAA PPL. In your case DAY VFR.
You can add an US Instrument rating, Multi engine rating or sea plane rating to your US certificate. But night flying is not a rating in the US so it can not be added after training. there is no such thing as a night-endorsement like a complex or high performance or tail wheel endorsement.
To legally fly as PIC at night you would need the night qualification on your JAA PPL prior to applying for the validation.
You can only legally fly night with an instructor.
If a flight school in the US told you any different, they are wrong.