I don't have any experience with this device, but this guy has. As Solar Mike states, it is probably on all the time and thus drawing energy. The 12vdc power is always on with one of the pins in the OBD2 port, so if that's where it's drawing from, it will always be on.
On some vehicles, if you tap into two of the pins (not sure which) at the same time and create a connection between the two, the battery light can come on. I don't know if that's what is happening with your vehicle, but it sounds reasonable.
With that said, according to the guy in the video, the device is a fraud. It's a placebo. It doesn't even communicate with the ECU. I have no reason to doubt him. Without specific/specialized software, you cannot arbitrarily change the tune in your engine. These devices are a complete rip off ... really, you get what you pay for (saw one on eBay for $2.05US ... heh).