Is it the shirt fit/material/style?
For reference the shirt is a brooks brothers regent fit shirt, and it doesn't change if jacket is buttoned or not.
For the fit you want, you need to use some sort of collaring agent when ironing. Mostly on the from part of the shirt but particularly on the top "triangle" among the collar and the top two buttons.
In Europe, I have been using a spray called Merito; surely there must be something similar in US.