Node.js express routers as middleware

Today I've encountered problem which got me confused for a little while as I expected routers work little bit differently and can't quite comprehend what is going on here.

Suppose I want to define my routing using express.Router. I create two routers, one for authorization purposes and another one for general routing as so:

let authRouter = new express.Router()
let generalRouter = new express.Router()

Next I define several routes such as login and dashboard routes with post and get methods:

authRouter.get('login', loginHandler)
authRouter.post('login', loginHandler)
generalRouter.get('dashboard', landingHandler)

After that I append both of my routers to the actual express app object:

app.use(authRouter)
app.use(generalRouter)

But.. I also want my website to redefine the way 404 works, so I create an additional handler for this case, let it be notFoundHandler, and then I add app.use(notFoundHandler) in case a request hasn't been caught by one of the handlers. Finally, we have this handling order:

authRouter.get('login', loginHandler)
authRouter.post('login', loginHandler)
generalRouter.get('dashboard', landingHandler)
app.use(notFoundHandler)

Turns out, last route is never reached and doesn't apply newly created rule for 404 error. I tried moving this line into generalRouter's handle list and it worked perfectly. But as far as I know, middleware is processing requests in order you define them, so there has to be no trouble with putting handler out of handle of routers, since by writing code this way I say "when these routers didn't respond, respond with custom 404 error", but it didn't work out. So. Does app.use(Router) shadow the remaining middleware or is it something else?