As far as I understand the refuge precepts come from two traditions: one from Asanga's and another from the 'Oral Tradition.' I am trying to find out what the Oral Tradition or as A.Berzin's site say the quintessence teachings are?
Are you asking about the two traditions of the Bodhisattva Vow, in Tibetan traditions? I'm not aware of two separate lineages of refuge, but there are two lineages of Bodhisattva vow.... Asanga's is known as the "Tradition of Vast Activity." Nagarjuna's lineage is that of the "Profound View," and was passed down via Shantideva.
I've seen the second tradition of the precepts appear in such works as Words of My Perfect Teacher with the three actions to be abandoned ie, taking refuge in worldly deities, abandon harming beings, and associating with non-buddhist philosophers and the three actions to be accepted such as respecting images of the Buddha, respecting Dharma texts, and Sangha or representations of them.
Then I have seen in addition to those precepts the precepts from the other tradition (Asanga's) presented in Tsongkhapa's Lam Rim Chenmo and which Alexander Berzin discussed about.