I'm not actually sure I see much of a dilemma here, to be honest.

Alignment is a nonissue. Breaking a single law, a single time, simply is not enough to change a person's alignment, especially if (as in this case) it is easy to defend within the strictures of the remainder of the law. Breaking a divine decree is a more serious matter, to be sure, but when the initial breach is accidental -more on this later- then attempting to rectify the mistake is certainly a Lawful thing to do. The gods might punish him for this breach, but his alignment should not change.

Let us next consider the paladin's code: the requirement to do no evil. By RAW, at least, this one's a no-brainer. He hasn't done anything evil yet, but leaving the situation be when he knows that this will result in planetary genocide certainly would be. Leaving is simply not an option. And as long as we assume the default paladin's code, that's all there really is.

However, let's assume that this particular paladin code includes an additional clause: the paladin has sworn as part of his code to uphold unto death a specific set of divine decrees, including this one. I would argue that this still does not conflict with the code, however, because the paladin has already broken the decree (albeit accidentally) by shooting down the hive ship: when it crashed into the planet, that constituted greater interference than dealing with the fallout possibly could. Going after the xill is not going to break the law any worse: indeed, he could argue that the prime directive demands that he attempt to correct the error.

My advice to the paladin would be as follows. Send a message as quickly as possible to whatever authority he serves under, to report that he has accidentally breached the prime directive. Explain that he is attempting to correct it, but because a Xill hiveship is involved, he requests reinforcements. Meanwhile, he will keep the authorities apprised of his whereabouts so that, once they arrive, they can find him easily. Once they arrive, he will submit to an inquest about the event.

This course of action prevents him from doing Evil while keeping himself as close as possible to being in line with the authorities. It lets him go down and kick some abdomen, while giving you an out in case things go wrong or drag out for too long: when the investigators/reinforcements arrive, they can handle the rest. Then you can cut to the paladin's trial.

In the meantime, I wouldn't say that he falls. The accidental initial breach cannot fairly be held against him, and as long as he attempts to correct the error and doesn't otherwise breach his code, I wouldn't say that this can either. On the other hand, if he tries to run away (by failing to correct the error or by failing to report his mistake), those could certainly be worthy of a fall.