No that is not the case. After one firing, your 45 ACP cases are not too long. I've loaded straight walled pistol cases many times and they never needed trimming. They ususally split at the case mouth and need to be discarded.
Trimming is usually necessary for bottle necked cartridges.
I don't know what brand dies you have but I will assume they are RCBS.
The first die is a sizing/decapping die which brings the die back to spec and removes the primer.
The second die is adjusted so that the expander plug flares the case mouth just enough so that the bullet will be easily started without crushing the case.
The bullet seating die is adjusted so that the it removes this flare and seats the bullet to the proper depth.
My guess is that you do not have the seating die down far enough. So you will have to back out the bullet seating plug a bit and srew the die in farther. I suggest you read the directions that came with the die or go to the RCBS site and print them out.