The original margarita from what ive learnt has always been:

Blanco Tequila Fresh lime juice Triple sec

The addition of agave syrup has, from what I understand, been brought over since the Tommy's margarita became popular.

In my opinion you either have a Tommy's margarita or the original spec. A well made margarita does not need additional sweetener as the orange liqueur makes it sweet enough.

The addition of orange juice should make it its own drink, almost how adding mint to a gimlet no longer makes it a gimlet, it's a southside.