When you attach a welt to a shoe, you necessarily must then attach an outsole to the welt. Normally, this outsole is a little larger than it actually needs to be, so it needs to be trimmed off – at some point. I have always been trimming the outsole and the welt at the same time, after it has been sewn on, as shown below:
There certainly is a certain logic in trimming the outsole after you have tacked it onto the welted shoe (but before you have sewn it to the welt) – it allows you to get a perfect fit to the lasted shoe, and when you are cutting your stitching groove, there will always be perfect alignment to it. I have always cut my grove prior to tacking on the outsole, so there is always a bit of “jinking” with the outsole to make sure the groove is set up properly, but it makes a lot of sense to trim the outsole first, and then cut your groove. In fact, Garsault also calls for this exact technique.
In retrospect, I believe the reason that I adopted the method of cutting the stitching groove first is that I had never been soaking the outsole prior to stitching, which made my life immeasurably more difficult! That washtub of water sitting next to all of those shoemakers in the illustrations is not mere decoration – it’s used ALL the time! =)