No, that shouldn't happen. They should be fine together. The only issue I can think of when it comes to keeping a Neocaridina and a Caridina in the same tank would be finding two species that like the same water conditions. Neocards in general prefer moderately hard (to very hard), alkaline water--ones kept in acidic water tend to have shorter lives and breed very poorly, with shrimplet mortality rates at nearly 100% if your water is too far down in the acidic range. Caridinas vary a lot more, but many of the most common ones prefer soft, acidic water, and you'll see nearly 100% shrimplet mortality rate if the pH gets above 7. All of the Tiger shrimps (Tiger, Super Tiger, Blue Tiger, Red Tiger) and all of the Bee shrimps (CRS, Crystal Black/Bee, Golden Bee, possibly Bumblebee) would fall into this latter category. That being said, there are certainly Caridinas that can thrive and breed in more alkaline waters too, and the Dark Green might be one of those. If it is, then you've found a nice combo for your shrimp tank.