I'm not sure if I understand your problem.
Regarding the main index at the Family tab:
You can choose the PRIMARY sort to be last name, first name, birth, marriage, or death order.
It sounds like you are using last name as your primary sort. The secondary sort when using last name as primary is already birth date - which is what you seem to be asking for.
In words, what you are asking for should be what you are seeing.
Maybe you can re-explain the problem.
BTW, the index that is obtained from the main menu (Person > Index) or the index from the index button at the mini-tree of the top of the Person page will NOT sort by any criteria that I have discovered. People with the first name of a certain last name are listed in helter-skelter order.
If that is what you are using, I can sympathize with you. I am often at work in the Person tab of the People workspace and want to select one William Smith from 75 William Smiths, but the index at the person tab does not list them in birth order. I have to switch to the Family tab to get the regular index in the left side of the screen - that one is always in birth order after the primary sort by last name.
Join me in making an enhancement request. The more poeple that join in, the better.