Salaried versus hourly pay has nothing to do with it. Labor laws deal with exempt (from overtime) and non-exempt.
A simplified explanation is: to be exempt, you must be able to set your own work hours. If you are not free to come and go as you please, you are probably non-exempt and are due OT even if you are salaried.
I said it was a simplified explanation, but you are correct it was too simplified.
In the cited source,. Administrative employees must,include the exercise of discretion and independent judgment with respect to matters of significance.
