There is an item in the field Properties box tab to the right of the "Basics" tab (the tab only appears for Keyword types and has a picture of a field). It's a little checkbox called "Refresh fields on keyword change".
In your "key" field, turn that little property on and your other fields will be recomputed upon an entry being made in the key field, just as if F9 had been pressed. The "key" field must be placed "before" (to the left and above) the fields to update within the form.