Why are two 555 timers in separate sub-circuits cross-talking? (Poltergeist in the Breadboard)
Why did you leave out C3?
From Charles Platt's Make: Electronics (1st edition):

There is a reason for everything in an electronic circuit (and Platt did explain why it is needed).  You have learned this the hard way.
From p155:

Set your power supply to deliver 9 volts. It will be convenient for this experiment if you supply positive down the righthand side and negative down the lefthand side of the breadboard, as suggested in Figure 4-14. C3 is a large capacitor, at least 100 µF, which is placed across the power supply to smooth it out and provide a local store of charge to fuel fast-switching circuits, as well as to guard against other transient dips in voltage. Although the 555 isn’t especially fast-switching, other chips are, and you should get into the habit of protecting them.

The comments and other answers have said you should use a decoupling capacitor of 0.1µF.  You can certainly try that, but you appear to have a long power supply cable and Platt has recommended 100µF.  So start small and increase, as in experiment.
To get it to work, you will need to link the circuits via R7.  IC1 fires IC2.

Why did Charles Platt leave out C3 in his second edition?
From p99 from Charles Platt's Make: Electronics (2nd edition):

A universal adapter such as the one in Figure 3-1 is the most versatile option, providing a switchable range of outputs. Typically these will include 3V, 4.5V or 5V, 6V, 9V, and 12V. Universal adapters are intended to power small devices such as voice recorders, phones, and media players. They may not deliver a perfectly smooth or accurate DC output, but you should be able to smooth the power yourself with a couple of capacitors, as I will illustrate when we get to a project that uses the adapter.

Not sure if he ever does that later in the book.  He considers four power sources: 9V battery; universal adapter with smoothing capacitors; fixed adapter with 5V regulator; and a benchtop power supply.  He states one of the the last three are essential.  Odds are the 9V battery gets discharged which impacts circuits working properly.
He is considering better quality power supplys, so he is eliminating the need for decoupling capacitors.  This really depends on users implementation of the power source and wiring.  He does not rule decoupling capacitors out, but rather differentiates between good power supplies and poorer.
10µF or 22µF on power entry and tight circuit will help regardless.  0.1µF in addition would not hurt.