Are employers responsible for car accidents caused by their employees?

Yes they are. In Florida there's a concept known as vicarious liability, or respondeat superior, which means that the master is responsible for the negligence of his servant. So in an instance where an employee is working, and in the course and scope of their employment with their employer and they get involved in the accident, their employer will be vicariously responsible for that negligence and any damages flowing from the negligence.