The built in method of plugins being able to be updated via the wordpress admin page requires you release your plugin to the wordpress open plugins platform.
If you have a plugin you want to keep private you have to find another way.
Private plugin updating resources
https://wordpress.stackexchange.com/questions/13/updates-for-a-private-plugin
Feel free to comment if you can add help to this page or point out issues and solutions you have found. I do not provide support on this site, if you need help with a problem head over to stack overflow.