I wondered how memory access is handled \"in general\" if ,for example, 2 cores of CPU try to access memory at the same time (over the memory controller)? Actually the same
There are dozens of things that come into play. E.g. on the lowest level there are bus arbitration mechanisms which allow that multiple participants can access a shared address and data bus.
On a higher level there are also things like CPU caches that need to be considered: If a CPU reads from memory it might only read from it's local cache, which might not reflect that state that exists in another CPU cores local cache. To synchronize memory between cache instances in multicore systems there exist cache coherence protocols which are are implemented in the CPUs. These have to guarantee that if one CPU writes to shared memory the caches of all other CPUs (which might also contain a copy of the memory locations content) get updated.