Yes - cisterns used to overflow to the outside of the property but now modern ones overflow into the toilet pan.
You might like to lift the lid of the cistern and adjust the water level to be an inch or so lower - operate the flush handle a few times to see how the mechanism works - you want the float valve to shut off sooner - don't forget to tighten the adjustment locking nut else it will happen again.
https://www.youtube.com/watch?v=GaR0ebeeJ2M
Very easy..., February 2015
