Try adding an include configuration for each site. betashares should work if you use its id, you can try the other site too but perhaps that UUID in the ID will change in future and thus prevent this approach from working for very long.
Ultimately, we need to work on Consider DOM autocomplete attribute values for form selection and field fill prioritisation · Issue #337 · kee-org/browser-addon · GitHub which will probably improve the behaviour for both of these examples.