"Overboost" is simply when the car sees more boost pressure than it has commanded. It is a tuning term, not a mechanical one. It is not very common that it happens, but there are many safeguards in place to ensure that if it does happen, the ECU takes precautionary steps to prevent any engine damage. The tune is very safe.
While the Stage 1 kit is a good value, bear in mind that the intake does not really add any performance. You'll be gaining low single digit horsepower gains at peak power. You'll be much better off waiting for the BNR V2 downpipe to come out, which should be in the next few weeks, and getting just the tune to start out: BNR Tune 2011-2016 Limited chevrolet Cruze 1.4L Turbo
I've been tuned for a couple of years and have put some very heavy driving through this engine. Make sure you're using a good oil (specifically, I mean AMSOIL, as most group 3 oils can't handle the stress the turbo produces when tuned long-term).
The boost threshold is set in the tune; I'm not entirely sure what it is though. The issue sometimes comes from inconsistencies in wastegate adjustments from the factory. Once those inconsistencies are accounted for in the tune with a datalog, you won't have anything to be concerned with.