The Star Destroyer is on it's way to Batuu, it hasn't found the Resistance's presence there yet. Rey says the location is not longer "safe"/"secure". Your evacuation is more of preemptive measure in case they do find where the Resistance has been hiding. A major battle ensues and the Star Destroyers in the system are crippled and you take a First Order Escape Transport back to Batuu. It's worth nothing that (at least on the toys of these vehicles) that these are actual pilot-able vehicles, not just pods that drop straight down, which means they could theoretically have gone anywhere, including back aboard the Resistance fleet which literally just arrived moments ago with some pretty major ships. It would stand to reason the First Order doesn't know where every single escape vehicle went (and we do see that there are plenty of them per Star Destroyer).
So, put yourself in the position of the First Order in the immediate aftermath of what just happened. The fleet you brought is crippled and the real "meat" of the Resistance has just arrived to engage you while a small handful of theoretical "new recruits" with probable limited knowledge just disappeared potentially anywhere (you certainly didn't notice in all the madness that just ensued), do you really devote enough of your resources back down to Batuu to investigate a group of newbies who may or may not even be there anymore or try to randomly bombard (the rather large planet) aimlessly? After all, most smart folks would probably jump planet once they had landed (and we have to remember that Black Spire is just one outpost on this planet, you could literally be anywhere). Or, do you choose to engage/chase down the actual Resistance that just arrived instead of chasing "scraps"?
The post-story more or less makes sense to me, especially when you consider that Kylo Ren and Hux are at a frequent disconnect in the films with how they choose to handle the First Order and how they feel it's resources should be allocated. Hux probably felt it best to pursue the actual Resistance fleet using the First Order's might than go after a couple stragglers who could be anywhere by the time the battle has ended (explaining why we do not see him further on Batuu). Kylo on the other hand, decides the issue is worth investigating further (which is why he still hangs around).
But at the end of it all, you need to suspend your disbelief to a degree and remember you are in a theme park. If nitpicking like that is truly an issue for someone, they probably shouldn't ride this awesome attraction more than once because in their mind, the events are happening exactly the same, twice, in the same canon. You just have to accept that you are re-living/re-experiencing a certain point in time in a larger story and take it for what it is worth. Heck, at this point in the timeline, Kylo shouldn't even have his helmet, yet he does. Some things you just need to let go, sit back and enjoy the ride. For example, don't be the guy who would stand up in the middle of a zombie movie and say to everyone "wait, this isn't right, zombies aren't real!". No. Sit back, suspend your disbelief and try to have a bit of fun for a little bit. There's enough worrying waiting for you out in the real world once you exit the gates.
