When it comes to oil finishes, not sure there is any real differences in finish techniques regionally. There will be slight differences between individuals, but there is nothing in this mix that would suggest any different techniques than what you would use with tung oil alone.
Basically saturate the wood and keep applying as long as the wood absorbs it (15-20 min). Then wipe dry and wipe any seepage periodically. Could be one application and buff, or repeated applications after each dries. Variation may be to apply with high grit sandpaper (400-600x) to create a slurry and fill pores to a degree. If one wanted to "build" with multiple layers, a light sanding between coats might also be advised
Calling this an "East Asian" oil finish is nothing more than marketing. Technically every finish with tung oil is East Asian. This is nothing more than a catalyzed oil mix with some bees wax. I also don't see any need for three oils, other than the BLO will darken the wood a little more than the tung.
If the BLO is being added just for the catalyzing components, I would skip the BLO and just add the catalyzer to the tung. As far as that goes, I see no benefit to adding walnut oil to the tung either. Maybe a three oil mix sounds more "exotic" to the unknowing consumer.
I was reading that asian techniques utilize many more coats which are applied more sparingly than is typical in the west, so this is what I was hoping to gain more understanding about. I also read that the oil is thinned, though the method of thinning is not clear to me. It goes wihtout saying that ancient Chinese wood finishes did not contain mineral oil or mineral spirits, though its possible they may have derived solvents similar to d-limonene from fruits.
My intent is to compare this product to what would be considered a conventional east asian/Chinese finish (assuming a distinction exists). I know conventional asian finishes wouldn't utilize walnut or linseed oils, so I planned to provide that feedback to him while also realizing he isn't necessarily trying to replicate a genuine east asian finish. He's never made any claims that this finish is supposed to be "authentic" or anything, and the formulation is consistent with other products he's developed.
Walnut oil is the base of most of his finishes. Ive had lengthy discussion about why he prefers it, and I tend to be on the same page as him. Walnut oil is similar to linseed in final appearance, hand feel, clarity, and cure time. Where walnut oil excels over linseed and especially over tung is its viscosity; its a much thinner oil. It penetrates deeper into the wood without dilution. It also does not amber over time like linseed. He also specifically uses English Walnut for his walnut oil, which produces a lighter colored oil than the California walnuts used by Mahoney's and Andrew Pearce. I have not been able to tell a difference once applied to Maple, but I suppose there could be a very subtle difference in shade with a darker oil. Walnut oil also does not create a white haze when cured like tung oil. So both he and I find it superior in many ways to linseed and tung. Is it as durable as tung oil? Doubtful, though Ive never compared durability. Most people using hand rubbed finishes are not overly concerned about durability anyway.
The walnut oil used in most of his finishes is double boiled, so it cures faster than raw oil. However, he has already confirmed to me that the walnut oil in this east asian finish is just raw walnut oil. In fact, the only polymerized oil used is the linseed oil, which he confirmed was to aid in the speed of curing. This finish also contains odorless mineral spirits to aid absorption. I think the use of walnut is probably just for better penetration.