Jump tracking could work because jumping is supposed to emit a burst of particles. If these have a directionality to them, then you could analyze that and see which direction the ship jumped. From that, you would know what star is in its path. The ship being pursued could jump to an empty hex instead, short or long of the star they appear to aim for, in order to foil pursuit. This is a good strategy - but they better have fuel with them for a second jump in that case as the chance of ending up close enough to anything to reach it before the air runs out is just a wisker above zero.
To track a ship you have to witness the jump occuring, which presumably means tracking the ship - as the rules suggest you need to be doing to make this work.
Therefore, no, starports can't see all the ships jumping out, unless they are in a small gravity well, and the ships are all jumping very close by, in which case they could theoretically manage it. If you don't want to share this information, just fly a little farther away.