Pop ups

You're not being a pain. Nothing will appear in that list unless you were to load a website that wants to open a pop-up window, and there is no way to manually add a specific website.

You can however choose to either block, allow, or ask — a choice that gets applied to all websites that are not specifically configured.

In your case you have a website that shows paystubs, so I presume you have to click on a link or a picture or an icon to view a particular paystub, is that correct? If you were to choose "allow" in that case the pop-up window should appear.

If you think it should, and it does not appear, first please determine if there is another window to choose from in Safari's Window menu — all the way at the bottom of that menu. Perhaps that window is being covered up by another.

On the left side, scroll all the way down to Pop-up Windows. On the right, you will see a list of currently open websites, websites that you already configured, and all the way at the bottom is a choice you can apply to everything else (When visiting other websites).

Also, when a pop-up window is requested, but you chose to block pop-ups, you might see an unobtrusive icon in the Safari Search field that you can click to display that window.

Refer to Change Websites settings in Safari on Mac - Apple Support, under Pop-up Windows.

You can enable or disable pop-up windows on a per-website basis, or globally for all websites.