So, it seems that once I go through a solar system, I can continue to see updates to that solar system, even when the probes or other ships leaves that space.

This makes probes and other passing ships too powerful. I think you should get a snapshot of what was there when the probe or other ship went through and only get real time updates when you send a ship back and park it.

If that's too complicated to implement, I would only have it keep record of the planets, not the ships, unless you happen to look when your ship is actually in that space.