People will care about the culture if they find their work and relationships meaningful. This type of culture can’t happen on its own. You have to cultivate it by empowering the people with the right attitude while letting go people that are a negative to the culture. This approach is the definition of tough love.
You should deeply care for the people that are working for you. Making it a safe environment where people are allowed to make mistakes. Then being there to support them while they reflect, or helping them directly to find a solution.