To reproduce:

Create 2 projects
Add a custom field to only one of the 2 project
Go to the simple searcher and try and add the custom field to the search.

This will fail.

If you select the project to which the custom field is associated, then the search will work.

Expected:

You should be able to provide nothing other than the search field you want to use. This is the same as using JQL to write customfield = abc. There is no need to specify a project or issue type.