I have just tried to replicate what you describe, but couldn't, so I can't answer your question. Perhaps it's a browser / operating sytem thing, which is beyond me, but I'll try and describe what I do in the hope it helps. At least it may get the ball rolling :)
My computer uses Windows XP and Firefox. When I have done the search on FMP and come up with a list of newspapers, this is what happens. Click on the result and a highlighted section of the newspaper page appears. I then have the option to 'download image' along the top of the box. Click on that and a new tab opens with the whole page displayed. There's a toolbar at the top and a 'download' icon towards the right hand side. Click on that and a box pops up 'Opening document.pdf' and asks you whether you want to open it or save it. I always save it for later perusal so click on 'save file' and the next box is the 'Enter name of file to save to'. It gives you the default name document.pdf, but I always change it to something I'll recognise later. Under that is the line 'Save as Type' and it says Adobe Acrobat Document. If you click on little arrow another line pops up saying 'all files', so perhaps that's where your other folder comes from. I make sure it says Adobe Acrobat and I always specify the file extension in the file name. In this case it's .pdf but in other applications you can choose, but I have found it's as well to make sure they agree! Then click on 'Save' and it seems to work.
Now, over to an expert .......?