Manufacturing of modern watches

Are the modern Omega watches now done by robots and automation and there is just a human that now just drops movement in and seals it and does QA?

No, still highly manually-intensive industry.
What you describe in your OP is pretty much what happens for the Swatch System 51 watches, but for most (probably all) Omega watches or similar, the watches are assembled by moving through a series of different steps, at which highly specialized technicians are completed their respective steps. Some on this forum may be even more familiar with the terminology of how the watch moves through the 4(?) major steps of watch production.

With probably the exception of certain models such as the Speedmasters fitted with Caliber 321 or for high end watches at indépendants, the lore of having just one watchmaker assemble a watch from A to Z (let alone to manufacture all the components), is just that: a myth.

They surely will never tell us exactly how much is automated and how much is an actual human working, but if you watch a few videos you will see robots doing a lot of work and humans doing a lot as well. Here is a few I have seen sure you can find more.