Hi Gage,
A few rogue black worms in your tank won't be too problematic and may even provide some enrichment for your newts as it gives them the opportunity to scavenge and hunt as they would do in the wild. But the worms will add to your bio load so if many escape that can be a problem (and I don't really know "how many" is too many. I think that will just have to be a judgement call on your end as you monitor water quality).
A deeper dish is a good way to start, but many people use "feeding jars," glass jars on their side that the worms are placed in and the newts learn to crawl into the jar to eat the worms. Another option is clearing away substrate from one area of the aquarium and placing the worms there. Worms will still crawl around, but newts are not dumb and will learn that the clear area is where food appears. Your newts will congregate there when they smell food and most of the worms will probably be consumed before they get too far. And those that make their way to hiding spots can then become "enrichment" as discussed above
HJ