But if those are really the URLs you're seeing now, that looks like some odd proxy setup — possibly unique to your institution? — that may not work with Zotero. (I'm a bit confused, though, because those look like proxied Ebsco login URLs, not even proxied page/PDF URLs.)
Here's a Debug ID D1752717406
I found a reference that doesn't work. Here's the link from the EBSCO (PsycInfo) results page, which clearly shows that the ref has a PDF attached.
https://web-s-ebscohost-com.erl.lib.byu.edu/ehost/resultsadvanced?vid=6&sid=66c08cba-e3fe-4de3-b1ba-49bbc96fe98f@redis&bquery=TI+religio*&bdata=JmRiPXBzeWgmY2xpMD1SViZjbHYwPVkmdHlwZT0xJnNlYXJjaE1vZGU9U3RhbmRhcmQmc2l0ZT1laG9zdC1saXZlJnNjb3BlPXNpdGU=
Here's when I click into the reference and it brings up the PDF inside EBSCO.
https://web-s-ebscohost-com.erl.lib.byu.edu/ehost/pdfviewer/pdfviewer?vid=10&sid=66c08cba-e3fe-4de3-b1ba-49bbc96fe98f@redis
There are other examples of ones that don't work but maybe start with these.