Babies can be experts at getting the m ilk off really quickly, much more so than a pump, so if he is only feeding for 10 minutes then that can be ok. When theya re getting fore milk, they tend to drink really quickly and guzzle, you can hear then gulping, the hind milk they have to work at and it is more like they are chewing the breast.
To increase your supply, pump more. It sounds odd as you will have to suppliment more from the freezer at first but since you are having to do that anyway it shouldn't matter for a couple of days. try pumping in between feeds for a couple of days and giving him what you express as well as the breast at the normal feed time and soon you will find that your breasts are a lot fuller. You shouldn't have to do it forever, once your suply is up as long as you empty the brest at each feed the supply should continue. If he doesn't empty you, express what is left at the end of the feed and save it or throw it to keep the supply up.