Jumping spiders don't really jump that high, it's more like a DASH forward with a very low arc (the jumping part is mostly to increase the range, at short distances or if jumping at a target below their own height jumping spiders travel almost in a straight line).
They do this so fast that they can catch flies, so it should be A LOT faster than this. It would probably work if you just make them lock on to a target (or the place where the target is while giving them a stun attack with a very small area of effect, so it effectively looks like they grab their prey) and then dash there - so basically having their path determined at the moment the start the attack.
This is a very good example of how a jumping spider attack looks like:
Also remember that a jumping spider will ALWAYS turn towards a victim before making a jump. They have exceptionally good (binocular) vision for arthropods and use their two huge front eyes to focus their prey before attacking (in fact their superior eyesight makes them so dominant in many ecosystems that they have forced entire groups of other spiders into nocturnal life).
