Would you believe I'm not even a tiler! I just make the tea for the lads on the forum.
I guess in a nutshell (I had a lot of codeine last night it must be said! My back is bloody killing me!) I'm saying it wouldn't be damp behind the tiles, which then might reach the surface of the grout, because it would be much more constant and equally spread.
When somebody has used dispersion (tubbed) adhesive behind huge tiles, and are having issues related to water not drying out, making the grout patchy, that's all it really does, make the grout look a bit wet, but sometimes it's not even wet to the touch. It just looks darker.
For yours to be so intermittent, and so strong when the problem is occurring, it HAS to be plumbing I'd say. Fresh water is being added behind the tiles when it's happening. And it's drying out fine after a period of time. So I wouldn't say it's a problem with a feed pipe (hot or cold further back than the mixer or whatever). My guess it it's either the drain, or the piping AFTER the mixer. So only when it's being used it's causing the issue.
The tiles just wont cause any problem like that.
When the guy re-grouted, if there was a bit of a puddle behind the tiles, the epoxy wouldn't have took so well as it has to have a dry surface to bond to. So he'd have raked the grout out, and if at that point he say moisture of any great amount, he'd have had to dry it out.