You cannot disable the function. The size of the image that is connected to the contact determines whether the image is displayed as a small photo next to the name of the caller, or as full screen.
I have individually cropped my contact photos to approx. 600x600 and added them via Contacts on https://icloud.com - this means that I only see small pictures there, and not fullscreen. It seems that Contact Pictures that I add directly on my iPhone become Fullscreen.
You can do as I do, or try opening the person(s) where the contact pictures become Fullscreen on your iPhone in the Contacts app, choose to edit the picture, and zoom out on the picture - and see if it makes a difference. Otherwise, I can guarantee that what I have done works, but it is time consuming.