That seems to me to be quite normal. My cats also get agitated when a "stranger" cat is around, even if the "stranger" cat lives in the same house. The cat is upset and lashes out at everything. You might try Feliway spray or diffuser, available from vets and pet shops. This is based on a pheromone/hormone and helps to calm cats. I find it most useful when a new cat is being introduced. The plug-in diffuser gives a continuous background of the calming substance, and a couple of sprays on the cat's bedding, or even the bottom of curtains keeps things "topped up". The substance is odourless to humans.