I was similarly perplexed by the Chinese-only taobao website. The photo at taobao showed the part number as "YB1602-OLED" and referenced a website yab-lcm.com, which is where there was a non-OLED display shown for this part number. Inspecting the taobao photos of the display (front and back), and your photo, convince me that you do indeed have an OLED display, and likely it uses the WS0010 controller. However, I cannot find in the WS0010 data sheet command table any inputs that adjust brightness as you indicate. I have used WS0010 displays made by Vishay in both parallel and SPI modes, and have had no problems with PBP's LCDOUT instructions sending commands or text to the displays.
Your inquiry asked why after changing brightness, you have to re-write to the display in order to see the effect. My guess is that this is just the way the display works. In my experience, I've found that display configurations are non-volatile, and the only way to ensure that old settings have been purged, and new settings take effect is to power cycle the display. Resetting a microcontroller and re-initializing the display while it remains powered can leave initialization artifacts.
I cannot find any reference to the command controlled brightness settings you provided in your earlier post. Do you have a Winstar app note that describes these? I have an OLED test program for WS0010 displays, and I would like to evaluate brightness settings.