ws2812 strips data grounding method & flickering
Do you've got a flickering of brighness, or flashing leds, which you don't wanted to light up?
If it's a data issue, you could try to short the data line to GND with a 1k resistor.
If the PSUs don't like each other, try connect them via an inductor.

Edit:

A friend of mine had the problem, that the LEDs were lighting up randomly without sending data. The wire at data-line worked as antenna. Pull-down helped. After more investigating the problem, we recognised, that there was a broken data line connector. Fixing it helped, because the µC pullup was enough to fix the signallevel on the data line. So grounding is not neccessary, if µC is permanent connected to data line.