@Luke FrankLin
Welcome to the forum. I have raised quite a number of seedlings, some of which were several different pines. So I have some experience, though not with JBP as they are not quite hardy here, so I focus on other species. The answer to when to repot depends to a great deal on your growing environment and your horticultural skill set. If you are south of St Louis, say in zone 7 or warmer. JBP are vigorous and grow relatively quickly. In the southern states, you can have seedlings that look as robust as the ones
@Thomas J. just posted. If you live in the northern tier of states, like I do, it may take twice as long to get that kind of growth, because literally you don't have as long a growing season. Usually I have less than 150 days to my growing season. Atlanta will have over 200 day growing season. If you have ideal sun and adequate water & fertilizer, JBP is a fast growing pine. If the position you have your seedlings is less than ideal sun, if you are not on top of your watering, if you are more like most of us mortals, and are hit and miss with out fertilizer, you won't get the vigorous growth you would want. So look at the seedlings in front of you, and decide based on what you see. Second year is a good time to repot for vigorous trees, 3rd year might be better especially if you are in the north, with shorter growing seasons.
Why repot? - repot once in the first 2 to 5 years to trim roots and begin training and shaping the root spread where the trunk and roots join, ''nebari'' is the term often used. Root base is good enough english name for it. You want roots to spread out radially, like spokes on a wheel. The sooner you start this training the better, year 2 or 3 is ideal, but if growth is slow, and roots are weak, it is okay to wait until later. Hence the 2 -5 years.
- repot if seedlings are crowding each other in the flat or tray or pot the seeds were sprouted in. If the seedlings are not shading each other, there really is no need to rush to repot. Group of seedlings in a pot will often grow better than just one seedling in a pot.
-repot if you want to do individual training and want to do different things to different seedlings.
Root cutting as referenced by Adair. That is a technique for more experienced growers. If you are new to raising trees from seeds, you will have very high mortality rate attempting the technique. If you are experienced, you will still loose 10 to 25 %, but if you were experienced, you would have started with at least twice as many seedlings than you wanted anyway.
It was either Jonas Dupuich, or maybe Mike Hagadorn, or possibly Peter Tea, maybe someone else, someone did a "study" of root cutting JBP seedling roots vs conventional trim roots at 2nd year transplant. Actually I think it was a blog potst from an interview by the author with one of the Japanese nurserymen who specializes in JBP, and they reported the nursery grower's comments. He compared 10 & 25 year old seedlings and commented that that many of the root cutting seedlings had nice radial arrangements of roots, and that the whole group of them were quite uniform, to the point of boring. Some of the 25 year old seedlings had to have some roots removed to make more interesting nebari to go with the rest of the tree.. All the roots were the same diameter, which did not look very natural. The ones that had not received the treatment were less uniform in their nebari, and some had really attractive departures from the "standard" radial arrangement. The ones that had not been treated also were bigger plants, with more growth because they did not loose one season regrowing roots. In the end,, the verdict was inconclusive. The root cutting technique created very uniform root arrangements, the trees without also had good root arrangements, but with more variations, but the number with "bad nebari" was quite low, normal root training techniques done at repotting time really were enough to create acceptable nebari.
So if you want to try cutting the roots off your seedling, having them regrow roots, it is an interesting technique, but it is not "mandatory", normal root techniques will result in decent roots most of the time.