For all azalea, and Rhododendron, it is okay to cut back hard and repot, prune roots all on the same day, as one single operation. Timing, the best response is probably in late winter or early spring. Don't not allow it to receive any frosts after this cut back and repotting. Done in late winter or early spring, you will not have any flowers, as you will have cut off all the buds. This is the preferred timing for the more rapid development of the tree as bonsai. This is the standard treatment for Satsuki, as outlined by
@Adair M
If you live in a climate that is fairly mild, with little or no freezing over the winter, or if you have a greenhouse in which to winter your azalea, you can as
@Shibui suggests, get away with performing this operation any time of year. I believe the more rapid development as bonsai will be had if you perform this pruning and repotting in early spring as suggested by Adair M.
I've retired for the second time, my spring schedule is no longer as hectic as it used to be when I was a partner in a blueberry farm. I will be going back to spring repotting for most tree species. I did learn to repot trees in late summer, usually in the July 15 through August 30 for my zone 5b area (first freeze is around Oct 15 ). Key is I normally do ZERO pruning after about July 30. I DO NOT prune at the same time I do late summer repotting. If I repot later than August 20 or so, especially trees that do not get repotted until Sept 15. they are wintered in a frost free well house for the winter. Repotting late in summer will make the tree susceptible to freeze damage. It will not be as cold hardy as normal.
I know myself I grow azalea for the flowers. Adair M is correct, it really is better technique to do your pruning and in early spring. What I try to do, is have enough azalea around that you have some you prune in spring, and some that you let have the "growing season off". The one's getting "time off" are allowed to bloom, then pruned later. This way more of my trees are being kept on the fast track to development. But a few are allowed to bloom, just to fill my need for something other than green leaves in the collection. As I have said, I hate boxwoods, they are boring, so I do let a few of my azaleas bloom each year. Key is, have enough different azaleas that you can have some bloom while the majority are on the "faster track" toward bonsai.
Myself, I winter my azalea by storing them in a frost free, zero light, dark well house. I normally leave my azalea outdoors, through several hard freezes. This is to force them into full dormancy before moving them to their dark winter storage. This also allows the ground time to cool to 45 F or less which is needed to keep the well house cool enough to keep trees dormant. Put them in the well house too early and they will not stay dormant. While waiting for the well house to get cold enough, I allow my satsuki to experience temps as low as +25 F. (about -4 C.). Satsuki are all over the map in the cold tolerance. The "northern Japan hybrids" can be hardy to +10 F ( -12 C.), yet the hybrids that originated in southern Japan might only be hardy to barely a degree below freezing. Vast majority are winter hardy to at least +25 F, so I use that as my "limit". There are some that say you can tell how cold hardy a Satsuki is by the shape of the leaf, there are enough exceptions that this is basically bullshit. You need to know the pedigree to know how hardy a Satsuki will be. By "pedigree" I do mean, know what the description in various nursery catalogs state as the expected hardiness is, often these catalogs will list the parentage. Satsuki books usually will tell you the hardiness of specific cultivars along with the parentage. Here is another reason it is important to purchase only known named cultivars, and don't loose the tag with the name. Buying "no tag, no name mutts" will always be a crap shoot when trying to figure out winter hardiness. Avoid "mutts" or if you must have a "no cultivar name mutt", don't be surprised if you guess wrong about its winter hardiness.
Safest to assume just a few degrees below freezing. Kurume azalea hybrids can be hardy to 0 F, or even colder, again depending on pedigree. (0 F = -17 C.) Key is to know the published cold tolerance of a particular named cultivar.
@QuantumSparky - this tree you pruned and repotted so late in the year, keep an eye on your weather, and avoid trying to "test" this tree's cold hardiness. It will not be winter hardy because of your late pruning and repotting. Hopefully where you store it for winter will have enough light that it can finish hardening off foliage before its winter rest. This tree will not be cold hardy, and will need light to finish maturing foliage before taking its winter nap. You are in Pennsylvania, the advice to prune any time of year came from "Frost Free area of Australia". Always look at the location of someone offering advice, and then ask yourself if that advice would work in your climate.