Error when registering an AngularJS controller dynamically in a separate file

Question

So I'm an Angular noob trying to introduce AngularJS to an already existent RoR environment.

Since it's a relatively heavy and robust web app, I thought the best way to go about it would be to write a controller for each section in its' own file (coffee, for the record), and load it with the view through $routeProvider, registering the controller dynamically by doing something like this (omitting irrelevant parts):

app.config [
   "$routeProvider", "$controllerProvider", 
   ($routeProvider, $controllerProvider) ->
      app.registerCtrl = $controllerProvider.register
      $routeProvider
         .when("url1",
           templateUrl: "url1.html.haml"
           controller: "url1Ctrl"
         )
         .when("url2"
           templateUrl: "url2.html.haml"
           controller: "url2Ctrl"
         )
         .otherwise redirectTo: "/homepage"

I load the main js file (and in it the above snippet) in the layout file, and each designated controller file in the appropriate view (that is dynamic, obviously). In each of them, I try to load the relevant controller using:

@url1Ctrl = app.registerCtrl 'url1Ctrl', [
   '$scope', ....., 
   ( $scope, ....) ->
     # some logic

Problem is, I get an error saying "Uncaught TypeError: undefined is not a function". I thought I was doing something wrong with the provider function but it seems I'm being a lawful citizen there. Also read a bunch of similar questions on SO:

How to separate Controller file in angularjs (basically using ".controller" instead of registering it? Didn't work for me)

Separating Controllers in AngularJS (same idea)

How to create separate AngularJS controller files? (same, but the controller files are always loaded, not lazy-loaded dynamically...)

Loading an AngularJS controller dynamically (seems like an over-complication?)

AngularJS Controller Not Registering (tried it, not the same issue i'm having, it seems)

Would love some input on what part of Angular I'm misinterpreting here.