I have 2 dropdowns that are created onOpen using Dojo/Dijit Select in my custom Web AppBuilder widget.
The first dropdown contains parent projects and the second dropdown contains a list of subprojects related to the currently selected parent project in the first dropdown. To populate each, a query is first made to a REST service, the results are parsed and then entered as a parameter into the function that actually creates the Dojo Select dropdown; Projects first and then subprojects. Here is an example of the Projects workflow, which contains an on('click') event to trigger the second subprojects query and dropdown creation: