What constitutes the two filters ``seeing'' each other?

When we say that circuit 1 ``sees'' circuit 2's impedance, this means that circuit 2 behaves like a box with some equivalent impedance across its input terminals. If you were to probe it at its imput terminals with some current or voltage, it would behave as if it has input impedance $\hat{Z}_{\rm in}$. Similarly, circuit 2 ``sees'' circuit 1 as a box with equivalent impedance $\hat{Z}_{\rm out}$.