Interestingly, when you provision a SharePoint Site, a content type Hub is automatically created and configured for you:

 

If you want to have automatic update, you just have to check the checkbox.

Now let’s have a look on what happen if you create a new site collection:

Then enter the parameters:

Interesting point to note, you can specify quota and also resources and you will see what’s left before you proceed:

then in this newly created site collection, have a look at the content type hub settings:

…so it is pointing to the main Content type hub.

Let’s try to do a change in one of the content type like adding a colon to a task: (TOTO in my screenshot):

Then publish the content type:

Then … you have to wait for the timer job to do the Sync (not sure if this is the 15 mn as on premise…) and you can see that the task content type has been updated in the site collection: