Crud can find its way from the hot water tank (bits of anode and calcium) into the cold water lines due to pressure changes when taps are opened and closed.
Similarly, that crud can be pushed into the pump head when city water pressure is then used.
When this crud blocks the one way check valve inside the water pump, city water can force its way past the check valve and fill the fresh water tank.
You did exactly right by removing pressure from the system and turning on the water pump. Water flowing through the pump can sometimes clear the bit that is holding the check valve open.
Lou and Laura with Bella - German Short Hair Pointer
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HAM CALLSIGN - KC3FFW