Just Because An Exercise Involves Something Doesn't Mean It's Being Challenged
An exercise that uses certain muscles does not mean it's optimal for those muscles. A squat "uses" upper body muscles, but no one does them on arm day. That means your standing band press exercises, whether it be two arms or one, still isn't much of a "core" exercise even if it's labeled such. If you want a real challenge to your "core" aka trunk/spine muscles, then lock everything else down and get at it. They have to be doing the majority of the work.