Spark when connecting battery module to DC power supply

I'm unsure if that's even an acceptable way to charge your battery. With that aside, the power supply probably has filter capacitors at the output and when you connect your battery to the supply the battery very quickly charges the capacitors - resulting in the spark.

One way to avoid this would be to power the PSU and set the voltage very close to the battery's own voltage, then connect the battery. With no voltage difference, there will be no sudden current flow. Once connected, you can wind the voltage up to where you want it.

Once again, this still sounds like a sketchy way to charge your battery. I'm just explaining my thoughts on your observations.

The spark is caused by your battery charging the output capacitor on your power supply, which is zero volt when you start and have very low impedance so the current consumption from the battery is huge the monent you make contact, i.e. big spark.

The easiest way to get rid of it is to place a suitable diode in series with the power supply and increase the voltage by 0.7 V to compensate, or 0.4 V if you go with Schottky.

Source: designed battery chargers for a living for six years.