Dendrites (ionic contamination) on home-brew PCBs
I am answering my own question as I was able to identify the root cause.

It is due to Flux. I am using Weller F-SW12 (datasheet)
I haven't experienced problems in the past because my PCBs were mostly for 3.3V/miliAmpere range (however, quartz filtering capacitors were often going crazy, now I know why).
The dendrites have appeared due to multiple factors:


High Voltages (relatively) - up to 16V
High Currents (relatively) - 30+ Amperes
Non-perfect Acetone bathing (for excess Flux cleaning)
Not washing final PCBs with distilled water


Normally, after acetone bathing I was drying PCBs. That process was leaving a thin layer of highly diluted Flux, thus spreading that Flux across the entire board.

I fact, I was able to recover "contaminated" PCBs by re-washing those with acetone and then intensively washing it all under the running water, finally rinsing everything in the distilled water.

To prevent future PCBs from dendrite formation I have replaced the Weller flux with simple rosin/alcohol fluid and have not observed dendrite growth ever since. Furthermore, this mixture doesn't require to be carefully treated/washed as is not conductive to electricity (It seems).