Is it possible to connect this 8x8 RGB matrix to espruino boards?

is it because module and espruino need to share common ground?

Yes - you could actually cause some damage by not sharing ground - but there's no reason you can't connect all the grounds together while still using an external power supply.

Introducing R killed other B or G pixels - as if red pixels suck all the power

It's quite likely - red LEDs run off a lower voltage than green and blue, so if too much power is being drawn and the voltage drops then you'd have trouble. I guess you could try scanning 3 times - once for R, G and B?