You design the different ammunition to work out of the same gun.

APFSDS for a rifled gun typically has a slipping driving band, so the subcalibre projectile isn’t spun as much in the first place. Once out of the barrel the fins tend to kill what spin there is, to a point. The braking torque from the fins will be proportional to the square of the spin speed so the projectile will likely still be spinning slowly when it hits the target.

How do HE and APDS share the same barrel, don't they require different twist rates?

If APDS and HE are designed to be fired from the same barrel, they don't need different twist rates. 

APDS and HE have been fired from common guns since the mid 1940's 

You might not get optimum of either with a particular twist rate, but you can certainly define a twist rate and design APDS and full bore projectiles to suit that.

Even if the finned penetrator is understabilised by spin alone ,it has fins for stabilization. 

Much longer projectile is obviously not stabilized by same twist rate as the shorter non ap projectile