Lets take the tech 1 warp core stab. It has an activasion time of 10 seconds. Does that mean its useless on any ship with an align time of more then 10 seconds, because it will switch of before you go to warp?
You just answered your own question…
It means it will run for 10 seconds.
In your scenario try aligning first and if possible getting up to 75%+ speed then hit the stab and trying to warp.
But like the above post said, they really nerfed the benefits of the stab.