Since you didn't show us what your g is, it is very difficult to try to reproduce your problem or to test possible solutions.
Is it possible that the evaluation process for NMinimize might evaluate data points outside the region 10<f1<f2<1500? The documentation appears to remain silent on this issue. But you could watch the process with the use of the StepMonitor option if you really wanted to verify this.
Since it appears that your g may include complex values outside your constraints, perhaps you could put your g inside a Piecewise function and have it return a large Real value outside your constraint region.