Well an x-ray wouldn't tell you much about the corrosion issue from the get go in general. You only would need a flux cored tig wire or solar flux if you weren't using purge gas. If those are the conditions you are using then you should not have corrosion. I would be willing to wager something has carbon though ...

In general rusting on stainless is not a HUGE issue unless someone has introduced carbon into the equation. Either through setting the stainless on carbon hangers, carbon pipe stands, used a cutting torch or a grinder near the stainless that throws carbon onto the surface, used a carbon or ss brush that was used on carbon, uses carbon steel hammers during fit up, etc.

Even then I've seen plenty of stainless joints not rust when carbon bull pins, hammers, and the like have been used. How soon after fabrication are the pipes rusting? Are they rusting after being exposed to process and if so what is the make up of the process of medium?

All the advice above is standard operation and needs to be followed.  I would add the following procedures that have prevented corrosion issues from my own experience.  There is a condition known as "creep" wherein oxidizing elements will migrate from the area immediately adjacent the weld zone during welding because of heat.  Unfortunately I can't give you any in depth explanation other than what I was instructed which was the neccesity to clean those areas prior to welding to prevent the migration of the corroding elements. 1" was the minimal rule as it was explained to me.  What I ended up working out for myself was as follows.  Prior to tacking the joint I used as barrel flapper disk the kind that works on a pencil/end grinder, and cleaned both inside and outside of the joint back at least 1.5" from the bevel.  Take the time to produce a uniform band of clean SS.  Weld the joint out until flush and ready for a cap and let it cool some [I always preferred to cap stainless when it was cool to the touch] and re-clean the 1.5" and of clean pipe next to the joint, back to its initial smooth clean band of stainless.  This will remove any oxidizing elements that have migrated toward the weld zone.  It really needs to be a smooth uniform strip of clean ss adjacent to the weld.  Cap the joint and complete it by going over it with a SS hand brush to remove color.  The hand brush was usually used in a drawing motion with a slight angle to it and mostly just on the edges of the weld.  I've followed this technique on 304/308/316 SS exposed to all kinds of the worst weather and joints I've welded doing so are still clear of any sign of corrosion 20 years later.  A thing I noticed over the years is that a lot of guys just give it a quick once over with the barrel flapper, you can see it's barely touched and the difference between the metal that's clean and the untouched parts.  Those uncleaned parts will allow corroding elements to migtate into your weld puddle and will produc rust at some point later.  BTW, the whole issue of "creep" and its prevention was introduced to me by a welding instructor who had spent a long part of his career working at the Hanford Nuclear Facility and was a seriously accomplished pipe welder as well as a tremendously competent instructor who trained a lot of nuke welders.  Lastly, a flat 4.5" flapper wheel wont do the job properly, you need to use an end grinder wheel and lose the wire wheel for cleaning, they are too abrasive and even the ones specified as 316 [most of them are 304 which has too much carbon] will leave corroding elements that will rust your welds. If you see any sign of a brown tinge next to your bevel prior to capping the weld, it is the indication of corroding elements that need to be removed before capping. My 2 cents.  Best of luck.