A "Smart Folder" is actually not a folder but instead a saved search. You can't add or remove items to or from smart folders -- you can only change the search criteria, which changes what they display.
Since a saved search is a single item containing only search criteria & not a folder containing files, when you put it in the Dock, it behaves just like any other single item in the Dock -- clicking on it opens it in its "parent" application, in this case the Finder. IOW, the result is a Finder window opens in 'find' mode showing the search results, not a stack springing out of the Dock.
I realize all this can be confusing to a new user or anyone else with little historic perspective of how the OS developed, but it actually does make sense from a usability perspective.
The Dock is a multi-function UI element that provides visual indication of which apps are open, convenient access to opening documents via dragging & dropping them on an app of your choice, ready access to your choice of apps that aren't running, various app-dependent options via the contextual menu that pops up from each application in the Dock, all in the applications section of the Dock. The other section is for shortcuts to your choice of items & where minimized windows appear.
The behavior of each Dock item is determined by its type & capabilities. An app is a fundamentally different thing from a document, a folder, or a saved search; it would be extremely confusing & unnecessarily restrict usability if the Dock treated each the same just because they each have a Dock representation!