It depends if your pop up is a custom code or just the native Toolset Maps PopUp offered when you insert markers.
If it's custom code, then it means that you use JS to fire a PopUp that needs to be re-initiated after the AJAX search updates the results.
With that we cannot help, because it is custom code - you could however fire your custom code again in those mentioned "front-end Events" that we offer in the JS Editor of the Search and Pagination section.
But it could be you mean the native Toolset PopUp that we offer when you insert a marker.
I am actually pretty sure it's the native one, because I can see it working well on the link you provided - until you filter - then the popup targets another marker.
I also see you built that with the Blocks plugin, so it's unlikely you used Custom PopUps.
I cannot confirm this issue on my own test sites with relatively complex maps that use such marker pop ups.
There, even using an AJAX updated search, the PopUp always appears at the right location.
This would mean the issue is only replicable on your site, or maybe I miss a step, OR, more likely, it's because my own online sites do not yet use Blocks (and will not, because they where built in older versions with features I cannot yet migrate to current blocks)
Locally, even with latest Blocks modes, I cannot replicate the issue you and me see on your site neither.
The popUps work great even if clustered and spiderfyed.
With Blocks, the approach is different than the "old" way, which Facebook User (XY) suggested you as well, but since native features seem used here, it should work on your site just as well as on mine.
I see the Blocks on your site have some issues as well, it says "this block contains unexpected content or invalid content" and asks to Convert or Resolve
In all honesty, I do not want you to do that, because I do not know what it cause and what will happen. This might be due to the beta state of the Blocks plugin, it might be due to wrong content, or anything else.
I need first to analyze this and ask our Developers what the intention is.
Also, doing so I will have a chance to actually check on the issue you mention, which I suspect to be an actual bug in BLOCKS, but not in the classic Views Maps.
So - what I suggest is, if you can, provide me with a copy of this site?
You can use Duplicator Plugin as explained here https://toolset.com/faq/provide-supporters-copy-site/
Then I can deploy that locally, and also send it to the developers for deeper analysis If needed, or provide you the proper solution here.
I activated a private reply, so you can add the data safely.
I prefer to not analyze this on your online site because it will require anyway some local debugging, and it's safer as well (I will not have to alter your online site)
Can you provide me that so I can deeper analyze this?