Install custom module into modules/custom folder
As I know Drupal web interface will always install modules to sites/all/modules.
Placing modules in subfolders like sites/all/modules/contrib, sites/all/modules/custom, or sites/all/modules/dev is a task for Drush and Drush Make; you can manually place the module in the right folder.

You can move your module folder with the PHP rename() function, or implement your own Updater instead of core ModuleUpdater. In your case, these solutions look improper.