Hi Tim,
Without the full structure of the call, I can't give a concise answer. We have found that postal codes that start with a number 1 or 2 can be aligned with a house number so it would be critical to use the specific designation to tell the geocoder that this is a postal code and for what country to disambiguate. For example the unstructured call:
https://atlas.microsoft.com/search/address/json?api-version=1.0&query=10012
-> This is a postal code in the eastern US but also a typical house number, worldwide.
As you are saying "Particularly in the US", are you designating the country in your call? Many places in the world have 5 digit building and postal codes so without clarification, the geocoder will do it's best but the more detail you provide, the more confident it can be.
https://learn.microsoft.com/en-us/azure/azure-maps/geocoding-coverage
For example you should be using https://learn.microsoft.com/en-us/rest/api/maps/search/get-search-address-structured and a call like:
https://atlas.microsoft.com/search/address/structured/json?api-version=1.0&countryCode=US&postalCode=10012
This tells the geocoder that you are providing a postal code in the US and then that information can be used to inform the result.
Sincerely,
IoTGirl