The answer turns on what the service is actually doing on the call, and the line that matters runs between veterinary telemedicine and teletriage. Telemedicine means diagnosing or prescribing for a specific patient. That requires a veterinarian and an established veterinarian-client-patient relationship, which in many states has to form a particular way, so no service can do it overnight without a licensed veterinarian on.
Teletriage is a different act. A trained professional judges how urgent a situation is and directs the owner to the right level of care, without diagnosing, prescribing, or opening a treatment relationship. Because it stops short of a clinical decision, veterinary teletriage does not depend on a veterinarian being on call, and it can take a caller on a weeknight, a weekend, or a holiday the moment the phone rings. So yes, a service can legally handle your after-hours calls, as long as it triages rather than quietly practices medicine. The test is simple: a compliant service assesses urgency and documents the call, then routes anything clinical back to your veterinarians.