After the Reset button is momentarily pushed, and then RELEASED, pin 3 of the Timer goes high for the timing period. When you initially connect the 9V battery, the timer comes up in the triggered state, just like you initiated a new timing cycle by pushing the button.
If it is the lower LED that is lit, and never goes out, this means the timer never completes its timing cycle. That could be caused by excessive leakage in the 150uF timing capacitor. If the current sourced through the ~2.5meg timing resistor is less than the leakage of the capacitor, the timing capacitor will never charge high enough to terminate the timing cycle.