I abhor the 'it's from China so it's fake' or 'Its from China so it's crap' mentality, while I'd not buy from eBay for a commercial project, as a hobbyist, it's an excellent way to get a huge variety of parts way cheaper than you can buy them anywhere else.
Yes there are fakes, there always have been even before eBay made it easy to buy from China.
There are plenty of NOS parts, there are plenty of 'refurbs' or pulls for sale and yes, there are fakes which aren't always easy to spot because sellers use pictures of genuine parts in a lot of cases.
Now, the XR2206, first thing, I suspect your PSU as it sounds like it'd be unregulated and possible even very poorly smoothed so chances are it's a *lot* higher output on low current draw.
Try it with a battery pack instead and see how it performs but before you do that, unplug the chip, grab a copy of the datasheet and measure the voltages where the chip will be fitted to ensure your power supply is correct polarity, correct voltage and on the correct pins.