App reference fields has the field type "app" as documented here. "Find items by field and title" can indeed only be used for searching app fields.
For a case such as yours where you need to synchronize data between Podio and another system, we recommend that you use the "external_id" of an item. When you create the item in the initial import you would set the external_id to something meaningful in the other system, e.g. the primary key.
Upon subsequent updates you can filter items by this external_id to see if you have that item already and then update it. Currently this is unfortunately also rate limited, but that's something we are working on fixing one way or the other.
Finally, if you must search text fields, you can try using the Search in app method.