I don't think they even go to the minor on "tremble", it sounds like they actually go to the dominant (they are in D, so it is A7) for an odd little bit of warbling by June before the line "Sometimes it causes me" and pop back to the D, which they hold onto in a very modal sounding fashion through the "tremble" thing--

The minor chord doesn't really need to be there--it just highlights the movement of the melody line--