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When would cores talk to cores like this is measuring?

Would two cores reading and writing to the same memory have this contention?

They mention that they measure "cache coherence protocol" throughput. So yes, this happens when two or more cores need to work on the same memory and they need to synchronize/update what is in their L1 and L2 (and probably L3 as well?) caches.

So cache invalidation? If core 1 writes to something core 2 has in L123? But who is responsible for that "correction", core 1 or core 2 or a combination?

On the totally basic principle core 1 will tell core 2 (say non-dirty state) to 'invalidate' it. At the same time core 1' and '2' can read a different value for that memory address/cache line before '2' carries the task. The protocol is more complex than that, the cache lines have different states. The basic protocol is known as MESIF[0] for Intel.

https://en.wikipedia.org/wiki/MESIF_protocol

Core1 would send a invalidation to get exclusive (write) access to that cache line. This would be routed to Core2. Which removes the cache line from its cache.

If core2 now accesses that cache line again, it would not find it in its L1, or L2, and at L3 there is the cacheline directory routing the request to core1.

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