The application begins with the routing stage. From there you grab the controller and action from the router, and feed it to the dispatcher. You set the view then call the execute the dispatcher so it access your controller's action. From there you create a new response object and set its contents equal to the view requests, and finally send the response to the client's browser -- both the content and the headers. It's a good idea to do this through Phalcon rather than echoing directly or using PHP's header(), so it's only done at the moment you call $response->send(); This is best practice because it allows you to create tests, such as in phpunit, so you can test for the existence of headers, or content, while moving off to the next response and header without actually sending anything so you can test stuff. Same idea with exit; in code, is best to avoid so you can write tests and move on to the next test without your tests aborting on the first test due to the existence of exit.
As far as how the Phalcon application works, and in what steps, it's much easier to follow the flow by looking at manual bootstrapping:
https://docs.phalconphp.com/en/3.2/application#manual-bootstrapping
At the heart of Phalcon is the DI, the Dependency Injection container. This allows you to create services, and store them on the DI so services can access each other. You can create your own services and store them under your own name on the DI, there's nothing special about the names used. However depending on the areas of Phalcon you used, certain services on the DI are assumed like "db" for interacting with your database. Note services can be set as either shared or not shared on the DI. Shared means it implements singleton and keeps the object alive for all calls afterwards. If you use getShared, it does a similar thing even if it wasn't initially a shared service. The getShared method is considered bad practice and the Phalcon team is talking about removing the method in future Phalcon versions. Please rely on setShared instead.
Regarding multiple views, you can start with $this->view->disable(); from within the controller. This allows you to disable a view so you don't get any content generated to begin with from within a controller so you can follow how views work from within controllers.
Phalcon assumes every controller has a matching view under /someController/someView followed by whatever extension you registered on the view, which defaults to .volt but can also be set to use .phtml or .php.
These two correspond to:
Phalcon\Mvc\View\Engine\Php and Phalcon\Mvc\View\Engine\Volt
Note that you DON'T specify the extension when looking for a template to render, Phalcon adds this for you
Phalcon also uses a root view template index.volt, if it exists, for all interactions with the view so you can use things like the same doctype for all responses, making your life easier.
Phalcon also offers you partials, so from within a view you can render a partial like breadcrumbs, or a header or footer which you'd otherwise be copy-pasting into each template. This allows you to manage all pages from the same template so you're not repeating yourself.
As far as which view class you use within Phalcon, there's two main choices:
Phalcon\Mvc\View and Phalcon\Mvc\View\Simple
While similar, Phalcon\Mvc\View gives you a multiple level hierarchy as described before with a main template, and a controller-action based template as well as some other fancy features. As far as Phalcon\Mvc\View\Simple, it's much more lightweight and is a single level.
You should be familiar with hierarchical rendering:
https://docs.phalconphp.com/en/3.2/views#hierarchical-rendering
The idea is with Phalcon\Mvc\View that you have a Main Layout (if this template exists) usually stored in /views/index.volt, which is used on every page so you can toss in your doctypes, the title (which you would set with a variable the view passed in), etc. You'd have a Controller Layout, which would be stored under /views/layouts.myController.volt and used for every action within a controller (if this template exists), finally you'd have the Action Layout which is used for the specific action of the controller in /views/myController/myAction.volt.
There are all types of ways you can break from Phalcon's default behavior. You can do the earlier stated $this->view->disable(); so you can do everything manually yourself so Phalcon doesn't assume anything about the view template. You can also use ->pick to pick which template to use if it's going to be different than the controller and action it's ran in.
You can also return a response object from within a controller and Phalcon will not try to render the templates and use the response object instead.
For example you might want to do:
return $this->response->redirect('index/index');
This would redirect the user's browser to said page. You could also do a forward instead which would be used internally within Phalcon to access a different controller and/or action.
You can config the directory the views are stored with setViewsDir. You can also do this from within the controller itself, or even within the view as late as you want, if you have some exceptions due to a goofy directory structure.
You can do things like use $this->view->setTemplateBefore('common') or $this->view->setTemplateAfter('common'); so you can have intermediate templates.
At the heart of the view hierarchy is <?php echo $this->getContent(); ?> or {{ content() }} if you're using Volt. Even if you're using Volt, it gets parsed by Phalcon and generates the PHP version with $this->getContent(), storing it in your /cache/ directory, before it is executed.
The idea with "template before" is that it's optional if you need another layer of hierarchy between your main template and your controller template. Same idea with "template after" etc. I would advise against using template before and after as they are confusing and partials are better suited for the task.
It all depends on how you want to organize your application structure.
Note you can also swap between your main template to another main template if you need to swap anything major. You could also just toss in an "if" statement into your main template to decide what to do based on some condition, etc.
With all that said, you should be able to read the documentation and make better sense of how to utilize it:
https://docs.phalconphp.com/en/3.2/api/Phalcon_Mvc_View