But they're exposed to the alignment of the celestial spheres in relation to the Earth the same way. Imagine if the celestial spheres have a particular electromagnetic relationship with the Earth, this dynamic nature is a type of 'song' if you will. That song becomes imprinted. That's one way I've come to understand these views. Then you actually have some semi-modern approaches to the music of the celestial spheres and the orbital resonances being similar to musical intervals.
Birkeland currents flow following magnetic field lines.
The Earth's magnetosphere is shaped by solar winds, rounded on the sunside extending 6-10 x Earth radius with a longer tail opposite the sun that extends up to 1,000 x Earth radius.
The Earth's radius is very small compared to the 1 AU Earth distance from Sun and smaller again compared to the distances between planets.
So, rather than "filling the entire universe" the currents you've linked flow through a magnet field that rapidly dwindles with the inverse square of distance and neither the electric currents nor the magnetic field reach to another planet (nor vice versa).