Scale eggs aren't in the soil. They're underneath the female on the plant.

The newly hatched scales are large enough to be seen.

The males are very tiny. You won't see them.

I would use cotton swab or cotton ball soaked in rubbing alcohol to get rid of the scale. If you miss one, there will be babies. You can also use spray of water+rubbing alcohol to be able to get into 'tight' spaces. The scale will come off easily that way.
How many plants are infected? Do you have photo?
Yes, scale will find it's way to other plants if not treated.
If you are using any soapy spray (or alcohol), keep plant out of full sun while doing it.

Rina

Thank you both for your responses, this helps a lot. I ended up keeping cutting small enough to clean well, and throwing the rest of the plant away. I think many were infected, but not bad, just signs of stickiness and a few visible females. I think I got them all, but we'll see. I'll continue with the soapy spray and alcohol if I see any signs of them. I still wonder how fast the males move because I had so many plants to deal with that they could have started wandering when I first moved the plants, before I took my cuttings, but so far no signs. On that note, I'm going to spray soapy water today to be sure. Thank you both again!

Be very careful with soap sprays on jade, which can be quite sensitive to soaps. Plus, scale insects aren't well controlled by soaps, certainly not home remedy and not even commercial insecticidal soaps.

Rubbing alcohol really is the most helpful product to use for scale insects on jade. I suggest a mixture of one part alcohol to three parts water, applied as a mist.

Don't worry about male or female scale. Some species don't even require males. The very small crawlers (babies) are not only mobile, but easily spread on air drafts, your fingers, and tools.

Thank you, rhizo, I'll use the alcohol solution, then. I always rub my tools with alcohol before I go to another plant, so I should be safe there, at least. How often do they have babies? Is it once a season or all year long?