99 KX250 Rear Shock Rebuild Query

What’s an oil cup?

Id say not necessary 

Kawasaki's service manual shows filling through the shock body..

The oil cup is then used to bleed the air through the compression damper's bleed hole...

The alternative method is to fill through the compression damper adjuster hole, and bleed before installing the compression damper...

or you can fill through the shock body, remove the compression damper and bleed through the compression damper hole.

Think it’s just for filling so you don’t introduce many air bubbles. I don’t think it’s necessary either

It’s called a …… 

I do it the way Last2Stroke's documentation shows.

The oil cup isn't necessary, but it can help you avoid making a big mess.

If you don't have the oil cup and you're working on a KYB shock, you can install the adjuster body far enough that the o-ring seals it up without installing the sleeve, the spring and the adjuster piston assembly.

You just fill it up as shown in those instructions, screw the adjuster body into the shock body to cap off that hole.
Stroke the shock a few times to get any remaining air out of the main-piston ports and shims.
Let the shock sit for a few minutes so the air bubbles can rise to the top and run the shaft in and out half-way a few more times.

Then remove the adjuster body and continue by topping off the oil.
I like to have a few pounds of air pressure in the bladder before I install it so it maintains its shape for final assembly.
When the shock is done, dump that air and charge it with 25psi nitrogen, dump that and fill to service pressure (145psi or whatever your spec says).