How will I know that the pet owner is located in a country outside my region?

From the Vetster web-app (while using Vetster on your desktop/computer): 

The pet owner's country will be noted in Upcoming appointments (link here) as well as within the appointment page, listed under Client information.

From the Vester for Vets mobile app (Android and iOS): 

The pet owner’s country will be viewable by following these steps:

1. Select the Appointments tab
2. Select the appointment you wish to view
3. Select Client & patient details. The country of the pet owner will be located under client city.