Do us a favor. Run one piece of brass through just the expander, don't run the ram all the way up. Just want to see 6.5 neck. Your dented case next to the neck up only.
I think the neck shoulder junction is further ahead on a standard 25-06 then a normal 6.5-06, so you are moving the neck/shoulder junction forward by simply sizing a 25-06 up to 6.5, and then trying to set the neck/shoulder junction back at least 0.040".
The dented case is much longer than the other case as well, are you hitting the end of the die?
Something else you can do is take the expander button and decapping assembly out completely and size a 25-06 case. You can see if you are moving the shoulders that way also. Usually form dies have several dies in the set, it doesn't try to do everything at once. I think you are doing too much with one press stroke.
Do you have the rifle? Or are you just making ammo? Any wildcat/AI rifle should be used in conjunction with your dies when you are making ammo until you figure out what you are doing and have a solid plan of attack. As a novice reloader, it sounds like you will learn lots from this experience, don't get discouraged.
Edit: thinking more about this, I don't think a 25-06 case sized without a neck job will result in anything. A good ackley chamber will only touch at - 0.004" below the neck /shoulder junction for a crush fit on factory ammo, so with a neck that is undersized it shouldn't touch a case unless there is a very serious flaw somewhere. You can always expand the neck only, then take out the decapping assembly and try moving the shoulder. You really need the rifle to keep sizing down until it closes with light pressure.