The popping, as far as I can tell, is definitely not related to the harness, and probably not the relay either. And yes, the pin 13 signal from the back of the HU has more than enough juice to turn on the ms-8.
Andy W. already explained the reason for the popping over at DIYMA, although it may have been in connection with high-level amp outputs, not sure. It had to do with a voltage differential between the speaker-level outputs, and the ground, IIRC, but I'm no genius when it comes to electrical things...
Mobridge DA2 > JBL MS-8 > ARC XDi 600/4 > JBL Gti 408 Mids & Vifa XT19 Tweeters; PG Ti2 1600.5 > Morel HCW-10 & IDMax 15