They keep it in line by curtailing or switching off generation. The generator typically still gets paid as if it were generating whatever it has available, which is perhaps an issue, but the total generation is reduced to meet the demand.
This is why there is negative pricing, it's cheaper to sell electricity in the negative than to pay a generator to be offline.
They can't direct excess generation to batteries if the batteries aren't there yet. They're being installed, but the overall capacity is still relatively low. Transferring it to other grids also has limits, and in particular if there's an excess of solar in one region the neighbouring regions also probably have an excess, so there really is no other option but to curtail.