I'll start out with a simple explanation and some others may wish to add more detail.
The pressure rise and heat in the compressors pretty much turns the water to superheat and the combustion process having far more air than it really needs just purrs on ... up to a limit.
Each drop of water must be converted to superheat vapor so this does place a significant load on the engine cycle which if not compensated by an increase in fuel flow will drop the RPM (although the actual thrust may increase due to mass flow effect.).
Most engines were demonstrated to run without blowing out at conditions up to 10% water by airflow. This in itself can accomodate extreme water ingestion conditions if the engine is operating at high power. However at low flight idle conditions the spool down effect on the rotors could lead to a flame out (several event in the records),
Methods of accomodating water ingestion include using the fan spinner as well as the bypass itself to centrifuge the water away from the core compressors. As well as increasing flight idle to a point where the spooldown effect still remains in a stable operating envelop.
Most of todays engines are expected to accomodate all but a E-8 storm providing you follow recommendations