I'm not sure since they do not provide any details in the manual you linked. no schematics, no part numbers for the leds, no nothing! without having the circuit in hand, it's impossible for us to tell why. if you say there is only the MCU,the RTC chip and a transistor, then that means the MCU must be supplying all of the current for the leds? that doesn't sound right. the next best thing would be that LEDs are digital as suggested before, so check if they have a connection to the positive supply. another thing you can check is the connection between the MCU pins and the leds. how many pins are connected? are they serial line pins or generic io? there's just too much information missing for us to tell anything.