I assure you, it is directly downloading it, but into a temp folder somewhere. The file cannot possibly open in Adobe Reader DC until and unless it is resident somewhere on your system's hard disk drive (or SSD equivalent). The behavior you describe is entirely characteristic when you have tweaked your web browser to open PDF files using the system viewer, as that will override what would be "the usual procedure" when a PDF target is detected. That target will be downloaded to a system TEMP folder somewhere and then promptly opened with the system PDF viewer, which must be Adobe Reader DC in this case.
There may even be a browser that would allow you to set specific file types to be opened by specific other programs that are NOT the ones chosen as the defaults under Windows 10, but I don't personally have any experience with any that do.
With the very rarest of exceptions, as corruptions can come into existence, these sorts of behaviors are the result of the interaction between settings that the end user, or someone who is/was their agent, set themselves.
Brian - Windows 10 Home, 64-Bit, Version 1809, Build 17763
Explanations exist; they have existed for all time; there is always a well-known solution to every human problem — neat, plausible, and wrong.
~ H.L. Mencken, AKA The Sage of Baltimore