I bought tokenized stocks on Solana. What happens to dividends and stock splits?

I swapped USDC and got a few tokenized stocks on Solana a few weeks ago just to see how they work.

The buying process was pretty simple. I didn't need a brokerage account, and the tokens showed up almost instantly.

But I'm still not clear on what I actually own. If someone else holds the real shares, how does it work when a company pays dividends or splits its stock?

Do those changes automatically reflect in my tokens? And what happens if the company behind the token shuts down?

Has anyone held tokenized stocks through an actual dividend payment or stock split? Did everything work as expected?