Well, I’m not so sure about the effect of 10uF on each of 10 modules (total over 100uF) on the 7812…
The datasheet says… 0.1uF for 78xx, 1.0uF for 79xx.
Also, the datasheet recommends clamping diodes when using a bipolar supply (“protects the regulator from output polarity reversals during startup”), and shunt diodes in some situations (which we may hit with such a big output capacitance…)
Peoples are questioning the utility of those caps on the modules, as I already pointed out here :
I still have no opinion on their usefulness/harmfulness.
Just make some tests with caps on your PSU but no modules…