How long does it take for Botox to smooth out Frown lines?

I received 20 units of Botox today for two frown lines- the provider told me that Botox simply prevents you from being able to frown therefore preventing wrinkle progression. But she stated I would not see any difference in the existing creases after the first treatment. She stated it may take up to 6 treatments before the lines are gone. My lines are pretty faint as I'm only 30. I've never heard this before and I was pretty depressed. Is this accurate?