Fuel cut is the ECU saying:
"The AFM is giving me a signal that is outside the acceptable range for the current RPM, intake temperature, coolant temperature and TPS value. In other words I've run out of fuel map and don't know how much fuel to supply the injectors."
As a safety measure, Toyota told the ECU when this condition occurs, just cut the fuel to the engine (shut off the fuel injectors). This really isn't a problem with a stock car, and would make the owner take it to the dealer. It's mainly to work around wastegate failures and unmetered air leaks.
There are a couple of ways around this for the MKIII, but the most economical and effective is method is to follow these three steps:
1. Replace your injectors with 550 cc injectors
2. Replace your AFM with one from a Lexus SC400 V8
3. Tune the car on a dyno with a wideband o2 sensor
This should allow you the freedom to run well past 13 psi SAFELY. There are Fuel Cut Defenders (FCD) and Boost Cut Controllers (BCC) available on the market, but I would recommend staying away from them. They simply override a safety feature by working in this manner:
They randomly drop a few pulses of the KV signal depending on KV level, TPS and RPM.
One of the problems with a BCC/FCD is it will also block out an unmetered air leak.
Wideband tuning is the key here folks. Simply put, if you don't know what your A/F ratios are, you have no business modding your car.
And if you are hitting fuel cut, you are flirting with disaster.