The book itself explains what it means (on p. 64):
Gambhiradarsanaparampara (Tradition of the Profound View), compliled by Manjusri, elaborated by Nagarjuna et al., propagated by Santideva
Udaracaryaparampara (Tradition of Extremely Vast Conduct) compiled by Maitreya, elaborated by Asanga and his brother, propagated by Atisa
tradition of Padmasambhava follows that of Nagarjuna
Later it says that the 80 auxiliary vows are in the Siksasamuccaya (Compendium of Precepts), which is by Santideva thus the "tradition of Nagarjuna". The mentioned 18+46 set is in the "tradition of Asanga".
The text itself is a Nyingmapa Dzogchen work that was commented upon by Dudjom Rinpoche.
Yes, so does this mean that the vows presented in the links given by you and Will is from the tradition of Asanga?
I have tried searching for an english translation of the Siksasamuccaya but have not found one yet. Do you know if such translation is available?
I remember having read a translation of it at sometime in the past. Now I found two english translations of it, both printed in India: Bendall,C.& Rouse,W.H.D., SiksaSamuccaya; A Compendium of Buddhist Doctrine (Delhi; Motilal Banarsidass,1971) Repr. Delhi 1990
Joshi,L.M., Santideva's Siksasamuccaya-karikas (Mulagandhakuti Vihara, Sarnath, India: Maha Bodhi Society 1965)