This is not how Roman succession worked. Especially at this time. This is a joke about the first Emperor Augusts. His biological father, whilst being pretty important politically, was not the reason he was able to turn himself into Emperor. A very basic explanation was that he got much of his power base from Julius Ceaser, who had adopted him, when he died.

So his biological father having any other children (which he in fact did have, an elder sister, who's own Son entered politics) would not matter at all. As the relationship with his maternal Uncle was where he drew his power.

This is all simplified, and I am no expert. But it is all much more complicated, and interesting (and always has been) than some simple rule of eldest son gets the throne.