Sounds to me like the car is suffering from a boost leak - either the plumbing has a leak somewhere or the wastegate doesn't hold pressure properly. Does the car have a boost gauge and if it does, can you see if you're losing boost at the same time you get the noise?
Normally you'll have a hard time hearing the wastegate if it's an OEM one as they all normally vent into the inlet tract rather than the athmosphere, so the first thing I'd check is if it has an aftermarket wastegate (and possibly boost controller). If it doesn't, I'd check the various hoses and pipes first to see if there's any boost leaks (you might have to pressurize the intake side for that) and fix those leaks.
If the car has an aftermarket wastegate, I'd check if it's a decent quality one as the cheap ones are mostly good for weighing down a trash can. If it is a decent quality one, you need to check how it's actuated - there is a chance that you have boost spikes that trigger the wastegate.
Edit: Thinking about this a bit more, I would start looking at the wastegate side of things first. If it was a boost leak in the piping, you'd normally just lose pressure gradually rather than having the boost build up and then get the "wastegate sneeze". My checklist would be:
- Check if it's got an aftermarket wastegate and if it does, check that it's (a) a good quality one and (b) that it's working OK.
- Check how the wastegate is actuated and if there's a boost controller somewhere in the mix
- Probably install a boost gauge if the first two steps don't lead you to a fix. What you need to verify is that you're not getting into an overboosting situation or get boost spikes that trigger this behaviour. If you do, you need to address what is causing these problems first.