For the managed package runtime, the Controlling Field Property on a Select Element can display Select Field Values based on the selection of another value from a Controlling Select field.
This information is for Omnistudio for Managed Packages. For Omnistudio on standard runtime, see Omnistudio Help.
Both the controlling and dependent fields must pull their field values from a field in Salesforce using the sObject property and those fields must have a Field Dependency setup between one another via Salesforce Field Dependency feature.
Example Controlling Field Setup
Controlling Field Configuration
Dependent Field Configuration
Defined Field Dependency in Salesforce
Using Option Source Custom
When using Custom as an option source, you can define an Apex class that will pull in the Picklist values source. See Populating Picklist Values From Apex (Managed Package).