It's hard to say, maybe the ballast that comes with the HID is of poor quality, there are many brands in the market, those cheapo brands from Brothers will sometimes have this problem, the lights will flicker. If adding a voltage stabilizer doesn't help, then the culprit is usually the HID set or do a comparison with the original lighting of your car then you'll have a clearer picture what went wrong.

Try checking your alternator to see if it's worn. Ask your mechanic to test it with a voltmeter. Worry that it doesn't have enough juice when the car is under heavy load like air cond, ICE and HID.

A good VS will help to solve this problem but your car's electrical must be in tip top condition, otherwise, it can't do miracles to your car.

Yeah, he's rite, buying a fakey VS will have an impact on your car's performance too. If you're going for Pivot, there's a guide for you to determine whether it is real or not from their website. Of course, not all brands are affected but for Pivot, the fakes ones can be found everywhere.

You can check minor things like the alternator belt too and also the battery terminals to see if they're clean or not. I believe it's just a minor issue causing this problem to your car.

Voltage stabilizers work on all cars, better voltage stabilizers will of course give you better performance, it depends on how much you're willing to invest for your car.