I added a local jurisdiction for AZ (Tucson) to my Nexus jurisdiction. However, no City tax is being added when I recalculate the invoice.
Depending on the address it may lie outside of the city limits. Therefore, city tax is not being applied. Using the address along with the zip code will give you a more precise tax rate. Using only the zip code may give you an incorrect tax rate.
In states like Arizona and Colorado- you may need to select applicable cities if you have selected "Selective" in the nexus settings (under select jurisdictions).