It's possible to interact with an installing service worker before its 'install' event is dispatched

Consider the following code, which results in the installation of a new a new service worker:

navigator.serviceWorker.register(script, scope)
  .then(registration => {
    registration.installing.postMessage('foo', []);
  };

In step 6 of Install, a promise resolution task is queued to the DOM manipulation queue; in step 10 a task that dispatches the 'install' event to the worker is queued. If the same queue is used, the then callback would run before the event is dispatch. (If it's a different queue, the user can't tell in which order these events would happen.)
This is pretty confusing, since a user might expect that an installing worker will have already been notified about it.

Start by tracing the Install algorithm at steps 6 and 10, including the promise-resolution and install-event tasks. Check how the relevant task queues are defined and determine the observable ordering for postMessage and the install event. Done means the specification gives a consistent, understandable ordering for these interactions.