Joseph: It comes from the Rambam who apparently said to wait “about” 6 hours. If you’ve waited 5 full hours, that means you’re in the sixth hour. Just like if you’re 25 years old, you’re in your 26th year. Some Sphardim I know wait 6 full hours for beef, and wait “into the sixth hour” for poultry.
So, yes, it means they start eating milchig 5 hours or 5 and a half hours after fleishig. I don’t really know with what area the minhag would be associated. I’ve never actually come across anyone who only wait into the sixth for all types of meat.