I'm not sure if you mean this video.
As you can see, at first he got almost the same lighting as yours. So, watch it again and looks closely what he did.
Also, If you want interior looks brighter under this light condition, the exterior should be a bit burned. It's normal.
I just took some shots from real life situation.
1. This shot looks very similar to above image and yours. (I focus on the sky)
2. If I focus on the drape inside the room, the room is brighter, outside is burned.
So, don't be scared to increase the exposure :D