The answer is never, followed by almost never during hydro test. The incidence of scuba tanks blowing up and killing people while being filled with air (or nitrox) is so rare as to be in the category of being struck by lightning the day after winning the lottery.
And what is a 'reputable' shop? I know of one very popular shop that simply looks in the tank, sees that there's no corrosion, slaps a sticker on, and rings it up on the register. I appreciate your sentiment that you would extend professional courtesy to another dive shop, but to be perfectly frank there's no real 'standard' or certification here. Any shop employee can simply put on the shop's sticker. Is it safe? Yes, but not because the tank is being 'professionally' inspected. It's safe because time has shown with millions of fills that filling scuba tanks to their rated fill pressure that are current in hydro test is a very safe operation.
So the fact that it's inherently very very very low risk to fill a tank allows the scuba industry to 'take credit' for this safety through the annual visual inspection practice. But outside of the U.S. this practice doesn't exist, and you don't see tanks blowing up all over the world.
I don't think it's a bad idea to annually look in a scuba tank; for example one wet fill can really cause some damage in steel tanks. I also don't fault anyone with a compressor who insists on doing whatever they feel necessary to ensure their own safety. But the current VIS program is little more than a fill tax IMO.
