That module has an LED, resistor, transistor and diode, so it just needs GND, 5V and signal to the
3 pin connector to work - which is what you did.
Its worth checking the correct voltages are actually getting to the relay module with a meter,
sometimes wires or connectors are faulty, and do a "close visual inspection" to check for
soldering faults etc (i.e. go over it with a hand lens in good light).
Another thing that strikes me is you are switching a pump, which is a highly inductive load.
Perhaps you forgot the free-wheel diode across the pump? That would explain the contacts
welding together for instance.