How are the year and month folders added to the uploads directory?

This is how I understand the process:

The wp_upload_dir() function is the main control room for the upload folder creation process and the wp_mkdir_p() function is the helpful assistant.

Everytime wp_upload_dir() is called, it’s actually running a file_exists() check on the current upload folder, through the wp_mkdir_p() function.
If the folder doesn’t exists it’s created with mkdir(), but not $wp_filesystem->mkdir() as one would expect.

The wp_upload_dir() function checks if the uploads_use_yearmonth_folders option is set. In that case the year/month folders are created, by default, from the current time of current_time( 'mysql' ):

// ... cut ...

if ( get_option( 'uploads_use_yearmonth_folders' ) ) {
    // Generate the yearly and monthly dirs
    if ( !$time )
         $time = current_time( 'mysql' );
    $y = substr( $time, 0, 4 );
    $m = substr( $time, 5, 2 );
    $subdir = "/$y/$m";
}

$dir .= $subdir;
$url .= $subdir;

// ... cut ...

// Make sure we have an uploads directory.
if ( ! wp_mkdir_p( $uploads['path'] ) ) {

// ... cut ...

where $uploads['path'] is assigned to $dir.

The wp_upload_dir() function is called within the _wp_handle_upload() function that’s implicitly applied during uploads. We also note that the media_handle_{upload,sideload}() functions are wrappers for the wp_handle_{upload,sideload}() functions, that are again wrappers for the _wp_handle_upload() function.

So I wonder if you might want to hook into these upload processes, using for example the wp_handle_upload filter within the _wp_handle_upload() function:

/**
 * Hook into the upload/sideload processes and check out the upload path.
 */

add_filter( 'wp_handle_upload', function( $args, $action )
{
    if( isset( $args['file'] ) && file_exists( $args['file'] ) )
    {
        // Upload path of the new file:
        $path = dirname( $args['file'] )

        // ... do stuff here ...
    }            
    return $args;
}, 99, 2 );

where $args['file'] contains the local path of the uploaded file and $action can be ‘upload’ or ‘sideload’.