However, it doesn't matter what the source is as long as the technique is useful for the end user.
Yoga, however, brought god back into the mix, and these days, when taught in India, it's mostly done in the tradition of Advaita Vedanta school, which is the vast majority of hindus.
Advaita means "indivisible", i.e. god, the world, and everything is one thing, but the very few texts of yoga that has survived, clearly show it was a dualist philosophy separating prakrti (matter) and purusha (consciousness).
Yoga itself however originated from Santana Dharma (or modern day Hinduism). To back up this statement, you can read this chapter of Mahabharata which talks about the birth of Ved Vyasa (the writer of the Vedas) wherein it mentions how the Sankhya, Yoga, Pancha-ratra, Vedas and Pasupati cults came into existence: http://sacred-texts.com/hin/m12/m12c049.htm
I'll quote the relevant text for your convenience:
"Vaisampayana continued, "I have thus narrated to thee, O monarch, the circumstances connected with the former birth of our revered preceptor, viz., Vyasa of unstained mind, as asked by thee. Listen to me once again. There are diverse kinds of cults, O royal sage, that go by diverse names such as Sankhya, Yoga, the Pancha-ratra, Vedas, and Pasupati. The promulgator of Sankhya cult is said to be the great Rishi Kapila. The primeval Hiranyagarbha, and none else, is the promulgator of the Yoga system. The Rishi Apantaratamas is said to be the preceptor of the Vedas, some call that Rishi by the name of Prachina-garbha. The cult known by the name of Pasupata was promulgated by the Lord of Uma, that master of all creatures, viz., the cheerful Siva, otherwise known by the name of Sreekantha, the son of Brahma. The illustrious Narayana is himself the promulgator of the cult, in its entirety, contained in the Pancharatra scriptures."
Not me, as written.
Also, I'm wondering how you got the impression that Kali Yuga = downward spiral. It is a phase in the endless cycle of the universe, but not necessarily a downfall.