Is this usual, or does it suggest I am using the wrong bullet (100gr soft points) through my .243?
There’s nothing wrong with the ammo you are using, so don’t start fretting about that.
In fact you shouldn’t worry about the fact both deer ran, either – it’s a normal reaction with a heart/lung shot, even though the animal to all intents and purposes is dead.
With this shot deer might drop on the spot, walk steadily a few yards before dropping or, as you have found, run a fair distance before keeling over.
Some while back I recounted a true tale here, which, in the circumstances, is worth recounting. It involved a professional ranger who shot a fallow deer with a .303.
The deer jumped a fence, crossed a grass field, jumped another fence and crossed a second field before falling dead almost 225 yards from where it had been shot.
When the animal was dressed out it was found the bullet had destroyed the heart.
From this you will gather that we will never really know how a deer will react to the shot – that’s why it’s best to always shoot for the heart/lung… it’s a large target and ensures a certain kill.