I spent time today reviewing the version 5.3.7 source code and may have determined why my newsletters are being sent to all subscribers in the site, regardless of the newsletter they are subscribed to. In the "run_for_time" function of broadcast_processor.php, there is a SQL query fetching the newsletter and subscibers of the current broadcast being processed. The WHERE clause of the SQL query does not appear to limit the results to the current newsletter only. In the code I reviewed, the query returns the subscribers for all newsletters. As a potential solution, I added an additional filter to the WHERE clause to check that the newsletter ID is equal to the NID variable ('newsletters'.'id' = $nid). I tested a few broadcasts following the change I made and it appears to have corrected my problem. I posted my findings here in hopes that Rajasekharan may be able to confirm what I stumbled upon and suggest whether or not this is a valid solution.
Thank you for all your efforts and hard work Rajasekharan!