As of today, according to the company, users who turn off the "Show the best Tweets first" setting will only see tweets from accounts they follow, in reverse chronological order (newest first). The new feature Twitter says it's working on will make it easier to toggle back and forth between the filtered and unfiltered mode.
"So, we're working on providing you with an easily accessible way to switch between a timeline of Tweets that are most relevant for you and a timeline of the latest Tweets. You'll see us test this in the coming weeks," Twitter said.
Several years ago, Twitter moved away from a simple timeline, adding "In case you missed it" and suggested tweets from accounts a user didn't already follow.