Is it necessary to use a ball spinner when applying a ball cleaner/polish like Reacta Shine to achieve the supposed 1500 grit polished finish or can it duplicated by hand as well?

I still use Lane 1 / Beans Sauce. You can apply it by hand and get a decent shine. It has fine abrasives and works as good as any other polishes I have used.

What's the best way to apply Reacta Shine to the ball using a spinner?  Putting it on the ball first or on a cloth first?  The bottle I have is a milky liquid that is very, very watery, and it tends to run everwhere.  Also, after it dries to a haze, is it best to use really firm pressure and "burn" it in to the ball?

The first very important step is to shake the bottle to insure whatever might have precipitated out, gets mixed back in. I'd bet you did not do this thoroughly, because the only truly watery polish I have encountered us Secret Sauce.
(Note: almost all polishes have the abrasive precipitate out of solution over time. That's why every polish instruction starts with "Shake thoroughly". Some are worse than others to mix it back up. Sometimes I have had to use a long flat balded screwdriver to get to the bottom and break up the precipitate. Some need to be shaken for an annoyingly long time.)

What I do for all polishes is to first apply some to the applicator; then use the applicator to smear it across the top half of the ball. This help prevent or at least reduce the amount of splatter, which is wasted polish. Once that is done, I turn on the spinner and work from top down the sides with light to medium pressure (depending on how much shine I want), spending more time on the side because that's the larger surface .

When I do this, I find very little dried haze and can already see the degree of polish that I want. Then I'll take the buffing cloth the remove whatever haze is left and buff it up.

If you want to burn it in to get a very high degree of shine, do that at the 1st stage where you're applying the polish. Start with medium pressure then use firmer pressure, but not so firm you stop the motor or even slow it down. Caution with the pressure. Use more polish for a more glossy shine.

Of course, if you really want a burned in shine, you should take the underlying grit level to 4000 grit and you should be using Xtra Shine.

Beans secret sauce on my old Track Slash did wonders for me. And I burnt my in

so like what charlest said, burn in the shine, just don't break your spinner like someone I know lol.

(Vertex bucket is molded to the shaft, the one piece broke internally and I tried in vain to repair this spinner for a friend. Everything else works.)

He must have been pretty strong. While I'm not real strong, I am large. I have tried fairly firm pressure on my 1/2 hp Vertex and I couldn't slow it down. I urge everyone not to put excessive pressure on any spinner. You don't need to do that to get a strong high gloss shine. As I recommended above, you need to work smarter, not harder.

Thanks charlest.  I do shake the bottles of polish before using them, but it didn't dawn on me that they would separate that bad.  My Reacta Shine has probably done this and is likely glopped together at the bottom.  I'll have to try a screwdriver and see if that's the case.

If it's really hard at the bottom, you'd be better off just buying a new bottle.