Scott,
Explaining this is semantically difficult.
thematic_init_navmenu() only registers a theme menu location.
This location is named the "Primary Menu" and is the one used by thematic_access() if a custom menu has been created and assigned to it using WP-dmin>Appearance>Menus>Theme Locations
The "Theme Location" input box does not even appear on the WP-Admin>Appearance>Menus screen until you have created a menu. So if you have not created at least one custom menu in the admin, you should so that you see what I'm talking about.
If you have registered more menu locations in your child theme and later hooked them into Thematic or called them from your templates, then you can make as many menus as you like and put them in whatever "Theme Location" you like using the admin.
So in answer to: "how do we designate a specific menu for that location"?
You do so by creating menus and using WP-Admin>Appearance>Menus>Theme Locations to connect the desired menu to your desired menu location.
and "how can we make certain it is the menu named "primary" that appears in that position"?
Assuming you have a function like this one included in you child theme's functions.php:
function child_access_navmenu() {
return "wp_nav_menu";
}
add_filter('thematic_menu_type', 'child_access_navmenu');
Then whatever menu you assign to the "Primary Menu" location in Thematic will show up wherever thematic_access() is hooked or re-hooked as it may be.
-Gene