+++ EDITED REPLY added some additional backup information about the programming language used to create the WordPress PDF Embedder plug-in
Is not confusing, I just can't help but notice that people in general use the term PDF interchangeably with Acrobat or "Adobe".
Embedding PDFs in Wordpress websites is a feature that Wordpress created, not Adobe Inc.
Yet, it is worth noting that the portable document format (PDF) technology that everyone have enjoyed for decades, even through the modern family of web browsers, was originated by Adobe.
My point is that, you need to contact Wordpress support; the Word Press PDF Embedder plug-in is platform independent as far as I am aware of.
As such, The inability to open an embedded PDF document in a new web browsing tab or in a new web browsing window, can be related to different things.
For starters, the Wordpress PDF Embedder seems to convert and weave together HTML code with ECMAScript, a part of the JavaScript programming language dedicated for web interoperability and also used as a compiler for other languages.
However, From what I've read, the majority of the code that is used with the WordPress PDF Embedder plug-in was developed in PHP (Hypertext Preprocessor); a scripting language that is sometimes employed as a server-side scripting language for web development.
Neither ECMAScript nor PHP are (in any way) the same thing as Acrobat JavaScript (which is based on extensions to manipulate and work with objects in a PDF document, not on web pages).
So we can't blame the Adobe Acrobat Pro DC software on the issue that you're wrestling with.
BUT, it may be possible that if you've created a secured PDF using Acrobat Pro, a core Acrobat JavaScript security feature may be enforcing some sort of restriction.
In addition, the free WordPress PDF Embedder version is limited only to uploading and embedding, and maybe a few other features.
So you may have to pay for the Premium version to have access to all the add-ons that you may be missing.
If you already are experiencing this issue with their Premium version then disregard all of my verbage.
But overall, my main observation is actually a question: In which web browsers is this happening?
Have you tested the same Wordpress page in Firefox, Google Chrome and the new Micrososft Edge web browser?
From reading further in the Wordpress support forums, some users have posted that when they click on the download button their embedded PDF opens in a new window instead of downloading the file directly to their computers.
As you can see, that is the behavior that you want, which for those users is doing the opposite.
Assuming that this issue is resolved by adding a button to that web page amd activating the appropriate add-on that you seem to be missing, you may need to review in your web browser settings if PDFs are defaulted to be downloaded or opened in a new tab.
That is also another setting that you must check which is not an Adobe Acrobat Pro DC issue and it is controlled entirely at the web browser level.
THANK-YOU! This is the most helpful answer I've received so far in all the forums I've queried. What this says to me is that my next steps are to check multi-browser functions as far as reactions to how the "target='_blank'" issue, and also to check WordPress plugin specifics, because I do believe some of the PDF embedders had paid upgrades that "allowed" links to be opened in new windows.
I sincerely appreciate the clarity, thoughtfulness and expertise you've conveyed in your response; this is a rare find in user help groups.