I finally found a few posts relating to this in the archives, and have to agree there's a problem. Someone had measured about 60?A of leakage when off - try measuring this on your unit and see how far it's off. At 60?A, this should last several months without charging - if it's flat in a month, that battery's not holding a charge as it's supposed to. (The Injoinic datasheet for their IP5303 says typical of 100?A quiescent current draw when off.)
IMHO, the charging system with the IP5303 is very wrong for the typical battery capacity of 0.4 to 0.45 Ah. Thus I'm worried about my battery now as I charge it. The battery, if you have a good cable and the power supply can do it, will be taking in a charge greater than 1C. This stresses the battery and likely will cause premature battery failure in cheap batteries.
The IP5303 is so inflexible that the only thing I can think of doing that doesn't waste charge energy is adding another battery in parallel, which will give enough load to balance out its seemingly inability to reduce charge rate for smaller cells. The IP5303 probably is expecting at least 1.5Ah of capacity or so, and likely less than 3Ah.
The power wasteful but simple solution is adding a resistor into the USB charging path to limit charge current. Maybe 0.33 ohms or so. This should improve the life of the battery pack, both cycle count and hopefully prevent pack failure, at the cost of charging time (and a resistor).