I have been meaning to sit down and list out everything that is known/suspected about core rocks into one document, so here goes. This pertains only to icy fields as I've not gone to metallic since the update, but I imagine the same rules apply.
1. Only certain in-game asteroid models can spawn with core deposits. I don't know how many different models there are exactly but I think it's around three to four.
2. I suspect that each model has it's own unique texture when scanned. One will appear with massive green splotches and transition to a bright red-orange. Another will appear with large dark patches and a black "net" over it before transitioning to a very bright yellow. There's certainly other patterns I haven't seen though.
3. The asteroid's model and the coloration of the scan seems to have no bearing on the type of core within.
4. Fissures or cracks are visible before hitting the rock with a prospector, just like how surface deposits are visible. This is the one thing that is consistent across all core asteroids, regardless of shape, size, scan coloration, etc.
5. Asteroids are persistent. This has been confirmed by others through various means. You drop into the ring at the same point, you will find the same rocks every time. What exactly this means for core mining, I am still trying to figure out. I have seen a post on this forum from someone who was core mining with no other ships around, but saw two vapor clouds from cracked rocks appear nearby, but with no debris, fragments, or ships in evidence. Their theory was someone in the same ring, but a different instance, had blasted those rocks, so the game removed them from all instances. If that's correct, then the more people mining a certain ring, the less core rocks you will find.
6. Core rocks do not seem to be evenly distributed. I have found half a dozen Void Opal cores within visual range of each other in one section of a hotspot and I have flown for twenty minutes, scanning continuously, without seeing a single core rock in another section. Sometimes it pays to get back into SC and drop in somewhere different.
Anything I missed?
More or less matches what i've seen except for one thing. I've never seen a rock that wasn't very bright yellow that had a core nor have i seen a bright yellow rock that didn't have a core. Its the only consistent thing i've found so far, although maybe that's just how the RNG has worked for me.
Also people saying they are popcorn rocks, that hasn't been my experience. You mention there may be 3-4 different types, at least one of those types i wouldn't call popcorn. Stupidly didn't record or take screenshot though.