Does this process happen when a user has a single account in three different sites initially and all three are below 200 and say after a year one of them crosses 200, so does the user get +100 for each of the three sites?
Yes, as I understand your question, you are correct.
If you are an experienced Stack Exchange network user with 200 or more reputation on at least one site, you will receive a starting +100 reputation bonus to get you past basic new user restrictions. This will happen automatically on all current Stack Exchange sites where you have an account, and on any other Stack Exchange sites at the time you log in.
You definitely get the association bonus on accounts that you already had.
You also, per the question you linked to, get the bonus on the site that "earned" it.