It's been awhile since I created this card but I don't remember any problems using the StazOn ink on the alcohol ink background. I do have a tendency to let my stamps sit for a bit before lifting off from the carsstcok so perhaps that was/is the trick.
Anyway ... here's the link to the card:
Sunflower and Dragonfly from Alcohol Ink Polished Stone BG by TeeGeeDee - Cards and Paper Crafts at Splitcoaststampers
HTH and ...
Tina aka TeeGeeDee