The most obvious reason you should take the safety information you learn at work home is to pass it on to your family. If your company spends the time to educate you about some safety concern that applies to home, you should also pass it on to your family. You do not know what you do not know, so educate your family so they are able to recognize hazards and protect themselves from harm.
Another reason you should apply the safety knowledge you gain at work when you are at home is to keep yourself healthy. Keeping yourself healthy allows you to continue to work and earn money for your family. Every person plays a role at work and even when someone gets injured off the job it hurts the company. Every company wants their workers to be safe off the job so they can return to work and fulfill their role in the workplace.