"What does the expression... mean?" is the correct way of phrasing this. "When the sh*t (impolite word) hits the fan" means: "When the result of what has been done wrong/poorly affects someone, later, with its consequences" "To run a tight ship" means: "To manage things very efficiently".

When the sh*t hits the fan is a phrase used for when plans do not go as planned. It is used with a fan analogy because if you imagine sh*t hitting a fan, it is thrown everywhere, meaning that not only one person is hit by it, but everyone involved is affected. Also, it means that when something goes wrong it will be hard to fix or clean up.