Nope, but it means your misinterpreting the blackbum, hehe
Its probably more liekly to be the patch of urticating hair just starting to become visible, you should be able to distinguish the urticating hair from the molting process because its only a patch of black as apposed to the entire abdomen turning dark.
No tarantula will molt so soon after a molt it would need at least weeks to recover, im not even sure if eggs with legs would ever be found molting so rapid, or even under a week so i wouldnt worrry about it.
Its just your T is getting hair in funny places, but it happens to all of them when they reach puberty

. Tell him not to worry, but his voice will drop soon too, lol