Good news, Thuja are pretty forgiving as far as horticulture is concerned. A little more difficult to bonsai, but easy to keep alive. (they are native to my immediate vicinity).
I have successfully repotted Thuja in winter, early spring, middle of summer, late summer and autumn all with roughly equal success. Only time I would not repot Thuja is in the middle of a spring flush of growth. Best if early spring, just before growth begins, or late summer after the bulk of growth has hardened off for the year.
Normally I would repot one year, do heavy pruning the next year. You ''might'' be able to get away with doing both at the same time but I think the best response from the tree is doing so in alternating years. More foliage will push stronger roots. Once roots are a year old, go ahead and work the foliage.
They do no back bud on wood once it has formed bark. Do not ''clean out'' all the interior growth, you keep the interiors to eventually replace the outer branches.