Sometimes off is not really off. It only takes about 650mV to turn on a small signal transistor like a 2N2222 or 2N3904. Transistor leakage is possible, but that is more of an issue at high temperatures. So the problem is that the base of the transistors is not going down close to zero volts, so they will be in a clean 'OFF' state, or some type of noise is getting into the transistor base.
Check make sure the MPU pins are at zero volts in the OFF state, and not just floating in a tristate mode. Check for ground noise, as ground bounce is the same as putting a pulse into the base of the transistors. It will show up on an oscilloscope or a good DVM set to read AC volts. Just to be sure that off is really an OFF state, install 10K resistors from base to emitter. When ON they will only consume 65uA from the MPU pins.
By the way, if the MPU pins connect directly to the base of the transistors without a 1K current limiting resistor, the MPU output can damage the transistors, or damage the MPU pin driver. Please double check this.