Usually the visual comes before the hydro. Why would you hydro a rusted or pitted tank?
I hear this a lot and I argued against the practice of doing the visual inspection prior to the hydro test at a shop/hydro facility I used to work for.
The regs themselves are silent on the order of the hydro and visual inspection portions of the re-qualification process, but the logic you present is exactly why most test facilities do the visual inspection first.
With steel tanks the potential issue is that the tank is then not fully dry after the hydro test procedure, so at a minimum the tester needs to look in and ensure it is dry, not excessively flash rusted, and has no visible contaminants.
With aluminum, and in particular 6351-T6 alloy tanks, doing the VIP first means that an incipient crack that is not visual before the hydro test may propagate further during the hydro test (where then tank is subjected to 5/3rds it's service pressure - 5000 psi for the average AL 80). I've seen this happen in a test facility where a visual plus/eddy current inspection was done on the tank with passing results and where the tank it self was leaking from a crack post hydro test. In this case it is fortunate the crack propagated all the way to a point of leaking, rather than just short of that and then leaking later. To be fair it needs to be pointed out this is a "normal" failure mode, and leaks are not catastrophic failures, so even if it had not leaked then and instead did so 6 months later, the results would not have been catastrophic.
But I digress - the point is that many RINs do the visual first - apparently based on the economics of time wasted testing a tank that will fail the visual portion anyway - and it's not safest possible practice. In steel tanks it's a moot issue if the tank is then at least minimally inspected inside after the drying process to ensure it's really dry, reasonably rust free and generally clean. And if not, the shop will catch a wet or rusted tank before it's a problem - but it may cost the customer the price of a tumble - and they will also catch any thing that may have entered the tank between being tested at the facility and being valved at the shop.
In 6351-T6 aluminum tanks however, I'd argue that it is a potential safety issue and in that case, VE stamp or not, the shop's VIP is a nice back up to catch the very, very small percentage of tanks that may have non-observable cracks that propagate to the point of detectability during the hydro test.
Ideally, the shop will de-valve your tank, do a quick inspection to ensure there are no obvious rust or corrosion issues that will cause it to fail the re-qualifiction before installing a shipping plug (or at least putting duct tape over the opening) and sending it to the test facility. The test facility will do the re-qualification (visual and hydro, and also a visual plus/eddy current inspection on 6351-T6 tanks), will again inspect it after it dries if they do the visual first, and re-seal the opening before sending it back to the shop. The shop will then do the actual VIP (and a visual plus/eddy current inspection on 6351-T6 tanks), re-valve the tank and fill it. And since they will mark up their cost for the hydro test by at least 100% (shop costs run anywhere from $7 to $20) they will throw in the VIP for free.
But most shops will unfortunately charge you a 100% mark up on the hydro, then stick you another $7 to $20 for a VIP, plus the cost of the fill and any totally useless (but costly to the customer) nitrox stickers/bands that they require. That can mean a hydro that cost them $10 will be marked up to $20 and then have perhaps another $10 for the VIP and $7 for nitrox tank bands, leaving you paying $37 plus the cost of the fill.
