You are absolutely correct! The chronology is followed by adding the fathers' ages when their sons were born. The Bible is actually more specific by saying "When Adam had lived 130 years", not 'When Adam was 130 years old. This phrasing continues in the genealogies in Genesis 5 and 11.
The genealogy takes us to when Abraham is 75 years old. Then we have a 430 year chunk of time spanning from when Abraham was 75 and set out from Haran until the exodus from Egypt, 430 years to the very day (Ex. 12:41).
The next chunk of time starts where the previous left off, at the exodus from Egypt, and spans 480 years to the laying of Solomon's Temple foundation (1 Kings 6). At this point the chronology goes back to the genealogies and the length of kings' reigns.
The video below takes a look at these and gives an overview and context to all of the events in the Scriptures. It also clears up some misunderstandings about the length of time the Israelites were in captivity in Egypt. Have a look at it! I've still got more to do on the exile before it's complete, but it's a good start to give an idea of the Timeline given in the Holy Scriptures.
https://www.youtube.com/watch?v=vqI7NMz0WcI