Hello Zbig
You’re absolutely correct. There’s no direct association between Tunnel 1 and the backup Tunnel 2. Notice that tunnel 2 exists between P1 and P2, it’s not configured in the PE (headend) router. This means that ANY tunnel that usually traverses the P1 → P2 link will be able to use the backup tunnel P1 → P3 → P2 for that particular link, as long as the local protection is desired by that tunnel (i.e. fast reroute of Tunnel 1 configured on PE1).
However, you must make sure that the bandwidth configured on the backup tunnel will be able to handle the aggregate bandwidth of the multiple tunnels that may use the tunnel as a backup. That’s part of the network design that you must take into account. Does that make sense?
I hope this has been helpful!
Laz