Last month, the property that I'm renting switched hands and I transferred everything to that company...so I paid the rent, but...the previous company still billed me for NOT paying the rent even though I did!

Should I pay them as well or call the new company that controls the rent?

If you feel you did the right thing, fight it.

Talking to the guy picks up my rent check every month, and here in Santa Monica and with rent control, we ALL get increases every year, not matter. But due to covid the people who lost jobs or "claimed they did", did not pay their rents and even due to covid the rent increases are waived until Sept I think my guy said. So the every June increase is not coming until Sept or so. The landlords are giving tenants a break. But he said a lot of people cheated the system too, claimed no work and could not pay rents....

Definitely don't pay twice. Let the new company know the old company that doesn't control your apartment any more went too far.

Yeah, totally don't pay twice ! Could just be a computer glitch, being the management company changed hands , there not on the role yet !;)