I see the difference in widths between the id="box_slideshow" and class="jb-splash-background" containers when I view your gallery in a narrow viewport (< 1024px), changing the user agent string in order to view the Splash Page, but I have been unable to replicate the problem in a test scenario of my own.
I embedded several galleries on a test page (gallery vs Splash Page, with and without a CSS margin being applied to the gallery container, with and without a CSS padding being applied to the gallery container) but do not see any discrepancy in the widths of the id="box_slideshow" and class="jb-splash-background" containers.
I can't quite wrap my head around the problem in your web page as you are using custom embedding code and there is a lot of external CSS to look through with many CSS margin rules (and I do not know how many, if any, are relevant to the problem at a glance).
Please take another look at your code (check all your CSS margin and padding values) to see if you can determine the cause of the problem.
I cannot replicate the problem myself in a stripped back example so the cause may lie somewhere within your code (and you'll certainly have a better understanding of your own web page's code that I do).
I can't be sure that your code is at the root of the problem but, being that I have so far been unable to replicate the problem, it might be worth another look.
Maybe its simply a case of the class="jb-splash-background" container not inheriting custom CSS being applied to the id="box_slideshow" container, in which case, whatever custom CSS you apply to the id="box_slideshow" container, you could also apply directly to the class="jb-splash-background" container. Not an ideal solution, perhaps, but it should t least result in matching widths.
The problem could also be due to the way that custom CSS is being applied.
For example, when setting Juicebox's height to a percentage value, it may be necessary to explicitly set the height of its parent divs via inline CSS (as noted here).
It is just a thought but if you are not already doing so, maybe you could try using inline CSS to apply your margin.
Again, I'm not sure about this at all, but it might be another avenue to investigate further.
I notice that you use setGallerySize(width: int, height: int) within onInitComplete.
Maybe this is the root of the problem and it would help to calculate the width and height of the gallery before the embedding code and then set the galleryWidth and galleryHeight within the embedding code (instead of afterwards via the Juicebox-Pro API methods).
I hope my notes above help to some degree.