Physiological speaking the connection part doesn't make sense.
In this chapter it was said that the chakra that flows into the brain affects the optic nerves.
If two eyes are separated they don't share the same brain connections or nerves.Rin implanted the eye to Kakashi and connected it to his brain and optic system.This is the main reason Kakashi has a physical disadvantage with the sharingan, his body is not cut out to have it.
Now on this chapter Tobirama said that special chakra flows to the brain affected by their feelings.Maybe the chakra is not special because it comes from the Uchiha's but because it is affected by the deep feelings.Kakashi too felt desperate and in pain when he killed Rin.Obito witnessed the scene at the same time.Maybe they both awakened MS at the same time for the same reasons.