How are auto-increment columns in the MySQL database coordinated across multiple instances of memcached?
They aren’t. There is no relationship between MySQL and memcached unless your application (or, if you are using the MySQL UDFs for memcached, your database definition) creates one. If you are storing information based on an auto-increment key into multiple instances of memcached then the information will only be stored on one of the memcached instances anyway. The client uses the key value to determine which memcached instance to store the information, it doesn’t store the same information across all the instances, as that would be a waste of cache memory.