Master Page Primary Text getting overridden

But now, when I apply a master page to document page, it doesn't use the primary text frame, and I get two extra text frames on my page, which I then have to rethread manually so that the story uses the primary text frame.

It sounds like you placed the text and set it to autoflow to the page margins right? Something like this where I'm placing to the margin and not into a text frame?

When you do that, InDesign creates page item text frames with no relationship to the masters, so in that case you wouldn't expect the text to find its way into the master page's primary text frame. If you had auto flowed the text into a master page thread, you could have gone to the master and set the frame as Primary by right clicking it.

InDesign makes a clear distinction between page items and master page items—you can detach a master page item (which is different than overriding) and convert it into a page item, but you can't convert a page item into a master page item.

It is being honored in that it is appearing on the document pages. Adding Primary Text frames after the fact will not affect already entered text. You must set them up before you enter any text on a document page. That is just the way that Master Pages work. To go one step further if you had set up text in a frame (primary  or regular) on the master page and then edited that text on any document page then it would no longer be controlled by the master. Also, as soon as you change the geometry of a frame on a document page or move it in any way it also is no longer controlled by the master.