You need more filtering. Remember the diagram I posted, with a resistor separating each unit from the power supply? Make that modification to the problem timer only, and be sure you have a 220µF on the 555 side of the circuit.
The RC time constant will tend to absorb the spikes. There are other kinds of filters you can use if this doesn't work, but likely it will.
The RC time constant will tend to absorb the spikes. There are other kinds of filters you can use if this doesn't work, but likely it will.