A personal umbrella policy will cover you if you injure someone or damage someone’s property. It is relatively inexpensive ($300 or so for $1,000,000 in coverage). The catch to getting one is that your home and auto insurance usually have to have pretty high liability limits to start with and you need to have them both with the same company.
The umbrella policy covers you when you injure someone in your car, boat or in another manner. But, it covers YOU for your personal liability. A personal umbrella policy usually excludes work related conduct. Generally, if you are working and you injure someone, your employer will cover you. Your employers insurance would defend you and not your umbrella policy.
If you have a specific concern about what coverage you need, you should consult legal counsel and an insurance agent. If you are just trying to protect yourself, talk to an agent.