How do I control my direction on the orbs in Titanic Monarch?

Acts 1 and 2 of Titanic Monarch include purple electrified orbs which fling Sonic around.

I cannot understand how these things work. I've spent so much time trying to maneuver myself in the right direction that I've maxed out the level timer more than once.

How do I control my direction on these gravity orbs?

According to the Titanic Monarch wiki page, these plasma spheres take their mechanics directly from the glowing spheres in the bonus stages from Sonic and Knuckles.

The Titanic Monarch Zone features a gimmick mechanics of reaching higher areas with the use of plasma spheres and Carnival Night Zone's side bumpers and teleporting fog. The plasma spheres take their mechanics from the Glowing Spheres Bonus Stage from Sonic & Knuckles.

From a Sonic & Knuckles FAQ, this is how these spheres work:

Hold left or right to change the axis of your orbit around the sphere (you orbit them like a planet orbiting the sun) from up and down to diagonal to side to side. Press A, B or C to jump off a glowing sphere, in the direction you were last going. To jump off really far you must time it to sling yourself off the sphere by jumping as you pass over it, after pointing yourself in the direction you want to go. It takes practice.