I think they also purchase it from elsewhen. At the moment, the fluctuation in demand is probably mostly handled by gas powered plants (because they're the quickest and most efficient to adapt). I suspect that green energy providers just need to meet the total demand over time for green energy, and end up paying gas plants for taking care of the fluctuations (because they need to buy energy when its expensive and sell it back when it's cheap).

If the green power providers produce exactly as much over time as the demand from their customers, that would mean some of the customers'money would still go to the gas plants, so I suspect the green energy companies produce a bit more, so they have some extra to sell to make up the difference.

It's absolutely true that until large scale efficient energy storage is real, green electricity will continue to depend on gas plants. Of all the fossil fuels, those will be the last to go, but that's okay, because it's both the cleanest and apparently the cheapest of the fossil fuels. But as long as there are still coal plants, there's still every reason to move forward with more green energy production.