That is correct, it all depends on your contribution settings at the time of the transfer.
If you contribute 100% to your family account, then the Amex transfer will also go straight to your family account.

I recently got an upgrade offer where it was a bit cheaper to upgrade from my individual account instead of the family account, so I set my contribution to 0%, transferred points, upgraded. Then I switched it back to 100% and a few days later, I upgraded another flight with points from the family account (again, after transferring from Amex), since the cost of the upgrade was the same.