How to create a more natural look using Strobe lights for watch photography?

You can define a preset manual white balance in the camera - Nikon D3500 manual, page 116

Assuming that fixes the white balance issue, you're still going to have to run these through Photoshop anyway.
You need to straighten, crop, remove the dust & scratches from the watch glass [unless you're selling them warts & all] & probably sharpen up a bit. I'd probably go for a narrower aperture too, to help the focus towards the back of the strap.

You're also a bit hot on the bezel, so you've lost information there.

I'm not sure you can get this task down as far as "click…sell" really. It is always going to need a little TLC in Photoshop first. This is my quick attempt at a bit of a cleanup, white balance, straighten (which still looks odd because of the strap), background set to white & a little sharpening & clean-up. You could do a lot better on the original full size photo…

BTW, watch hands are traditionally set at a few seconds before 10 to 2 or 10 past 10. 13 minutes past 9 looks a bit odd.
You also need to make sure your watch face is absolutely square-on to the camera; you've got a slightly elliptical look to it as it's tilted back. Strap top & bottom edges need to be parallel too.

You fill the dark areas by filling that space with more white material in line to the reflection. With anything that's virtually 'colourless shiny silver' you have to make some artistic choices as to where to throw light & dark into the reflections so you don't lose the essence of the shape. Your lighting setup seems to do reasonably well on most of the body & strap (I'd perhaps raise the centre of the lighting a little to make it appear more lit from the top), but the bezel is problematic. This, for instance was a nightmare to light against a black background. It ended up inside a large square box made of white backdrop, bed sheets & soft-boxes, with judicious dark gaps left so it didn't lose the heavy shaping of the front & sides.