My 2 year old nephew has the same leaking problem with his disposable diapers when sleeping on his side and his mom puts plastic pants over his disposable diaper to help contain the leaks.
I know you're asking about adult diapers and he wears Pampers Cruisers at night but the same thing should work for your Adult Disposable diapers.
Try placing some plastic pants over the disposable diaper and make sure you pull out the standing leg gathers that go around your legs and be sure the diaper isn't fitting too loose around your waist and legs.