Gorgeous photos! I love them. I do agree with you that the photographer definitely did some heavy vignetting.
There are lot of different ways you can adjust these photos that would yield a similar result. Here is a screenshot of a two click adjustment I did in LR.
Develop > Add Mask (shift-w) > Add new mask background > move exposure bar to the right
Alternatively in PS, you can use a curves or levels adjustment layer so you're only targeting the edges of the photos and not over-exposing the subjects. Same concept, different tool. You can use the subject select tool or use your eraser tool to hide the exposure on the center of the photo.
Select > Subject > Inverse > Curves adjustment layer from the layers palette > pull the curve up
