Actions actually don't work very well when you use grid edit, they especially don't work if you are editing more than 10 records at a time. This is due to the limitation of 10 triggers per second on the actions.
Its in the documentation, but QB doesn't like to advertise that their feature has a serious flaw in the execution.
If you are going to be using Grid edit, you will need to use a webhook, and a server script that will evaluate all your new records, and run the import to the other application.