Like Willy says, mining starbases are galaxy wide and all other starbases only affect the area inside their circular "area of influence".
One thing is that the constructor circle hasn't always lined up with the circle around the starbase once built although that was probably fixed long ago. However you still need to note that if the circle just barely covers even the smallest fraction of any particular parsec then that parsec receives the starbase bonus.
The following diagram shows this more explicitly. The X is the location of the starbase, the green circle is the "area of influence" and the red polygon outlines all parsecs that receive the starbase bonus.