The Black Bushing Just below the knurled top the springs are seated in with friction fit are what is being refrenced her. The reasons are simple. By turning the bushing anti clockwise and holding the tower you are raising the plinth without creating torque on the spring and damaging it so the spring only sees vertical force balanced in both directions and not horizontal torque. Think of twisting a slinky and what that does to its ability to return to its proper shape.
The reason you turn the bushing and not the tower is so the aluminum disc at the base of the tower the spring is attached to can rotate freely on the teflon washer. Torque or twisting would spread the spring at its base thus destroying the spings ability to work as designed. Thats to not damage the suspension as well as to "raise" the plinth to finely adjust level and the suspension bounce evenly.
If you look at how the spring is is fitted in the aluminum disc the teflon washer sits on and carries the weight of the plinth you will see that by turning the bushing counter clockwise the base of the spring will not be affected by torsion twisting as the spring will tighten around the aluminum disc so it moves as one piece and applies a balanced weight / compression without torquing the spring and distorting it.
If you do it the opposite direction the balanced weight/ compression ( designed to balance the load it carries with the springs natural need to compress back to its original shape) will become torque and will not tighten around its aluminum retainer bushing or tower base and instead spread the last ring of the spring or more likely the middle at its weakest point when stretched from weight and torqued from turning thus destroying the springs ability to travel smoothly up and down freely. The design of the springs requires proper adjusting use to avoid damage.
Having the beginning of the springs all pointing in one direction which is towards the centerpoint of the weight they carry ie ) the bearing is logical in the sense that they will all react to the weight exactly the same way and the shock of vibration travelling through them.
You will never comlpetely remove all side to side movement as the springs need to be lighter in gauge to properly work. Properly set up the table will bounce in a way that while playing you can push down on the clamp knob and the table will still play perfectly while dissipating the added force till it stabilizes to its own weight and the downward force of it with very, very minimal side to side movement. Check your springs and see if they are visibly distorted. You can tell by the flow of the spiral if they have been damaged by improperly torquing them. I know this does happen as I bought a used Orbe and could never get the suspension to work as smoothly and properly as my Gyro. I took it apart again and sure enough 2 of the springs were distorted. I ordered a new set and problem solved and works as it should.
The other things I could suggest that may be part of your problem I will suggest as possibly:
1/ The base when set up was not set up where it is being played and not perfectly level if it was.
2/ Not knowing your arm and mounting plate used you may have exceded the 1 kilo recommended weight making that corner of the triangle heavier moving the center of mass
3/ The arm and cartidge were not set up completely and correctly before raising the plinth off its level base to suspend it.( changes made after the fact)
4/ The base and the plinth are not perfectly horizontal, level and paralell to one another.
5/ One or more of your springs are distorted out of shape from torque and not compression.
6/ The belt is not level when table is at rest. Regardless of what others may argue it will only effect speed and playback the table is trying to drain energy to find its level at resting point and a belt not level at resting point will interfere with that as the motor is seperate from the suspension but the belt is not.
7/ The table is not properly isolated from a suspended floor, deflection the table see's more on one side depending on direction of joists. This throws the table out of level then back creating horizontal and not vertical movement.(Rare but happens) Opposite of a footfall wih floor deflection infront of the table that throws it out of level front to back. Both will create some side to side movement as the table stabilizes.
8/ Your phono cable from the arm is not allowing the table to move completely free .
Difficult to do anything other than guess without seeing it but from your description the suspension cannot be tuned properly or you mistakenly believe that suspended tables travel "perfectly" up and down with no side to side movement. They all do but set up properly it is simply so minimal and definately not exagerated to effect playback at all.
Hope this helps you understand how they work and why anti clockwise turning the bushing when tuning with weight applied on those springs is necessary. The compression from the top of the spring and weight on the spring from the table are meant to stay static and the adjustment is to fine tune to level by "raising" the plinth. Thats part of the idea for the 1 to 2 mm to leave minimum adjustent to prevent bottoming out and leveling and reduce travel to minimize side to side as well. If you have any questions just email me.