AZZA is not completely "no name" PSU maker - it's relatively new /or I think so/ but has some quality products.
FX-9370 is essentially no different from 8320, same product only default frequency setting is higher. So, your mobo will most likely recognize it as 8xxx and run with it even if it's not officially supported /meaning not tested or not supported because of some manufacturer politics or a third possibility I'll mention later/ but at lower frequency, so you'll need to manually set it for higher frequency - like "overclocking" it - only difference - you'll know your CPU guaranteed may go up to at least it's default speed.
What's the problem with your mobo and why it doesn't officially support that CPU? The only real problem is with the extremely high TDP of these processors. By the manufacturer it's set to 220W /or was it 210 - not exactly sure/ - and this mobo can't deliver so much power to the processor. But the real TDP of your CPU will most likely not go even close to that "official" number. Actually it'll be the same as if overclocking a 8320, because they are essentially the same thing - only yours is tested on higher frequencies so most likely it's "better" - able to run on that frequ. with TDP below average for the 83xx parts. And Yes - you may have a bad chance to have a not so good piece of hardware who runs too hot and needs too much power which will put you in a bad situation, but that possibility exists more or less for everyone with every piece of hardware even within the frame of completely "legit" parameters. The main reason for AMD to set so unnecessary high TDP value for this particular piece is essentially politics - they have in this series besides that model just one other with higher Thermal Dissipation /TD/, respective needs for more power to be delivered to it, too high price and probably only limiter footprint on the market, so if they set this TDP number only for it they are affraid there may be no mobo manufacturers to actually make certifiable mobos for it - so they set the same very high TDP for the lower part /yours/ too to force manufacturers to make mobos delivering this much power if they want their hardware to go through certification...
Note: Only something to be more clear - TDP is not only about the temperature, it means bots heat dissipation and power draw, and what concerns the mobo more about it, it's the power draw.