It is true that the insurers of which I’m aware want you to have both home and auto policies with them before they will write you an umbrella policy, but the usual umbrella policy is not limited to kicking in after regular coverage is exhausted.
It also covers other situations, such as personal liability and vacation rental. From the Progressive site:
An umbrella insurance policy extends well beyond your home and auto insurance if you're found liable for more than your other insurance policies can cover. A personal umbrella insurance policy allows you to select a liability limit that best protects your assets, up to $5 million. Umbrella insurance coverage may include the following:
Personal injury coverage: For claims of libel, slander, defamation of character, and more
Worldwide coverage: For incidents that happen abroad
Vacation rental liability coverage: Protection for accidents involving boats, jet skis, scooters, and other rentals
Defense coverage: For legal fees and court costs
No, an umbrella policy would cover this.