Merkle signature + PRNG?

In the section 3 (page 44) of the book "Post Quantum Cryptography", it says:

Then each one-time signature key must be generated twice, once for the MSS public key generation and once during the signing phase.

Also defined $\text{PRNG}$: $\text{Seed}_{\text{in}} \rightarrow (RAND, SEED_{\text{out}})$, where $\text{RAND}$ is a random number.

Finally, it describes an example of MSS + W-OTS. Here, $\text{SEEDOTS}_j$ is used to generate signature key $X_j = (x_{t-1},...,x_0)$ where $x_i$ are generated on $(x_i, \text{SEEDOTS}_j)=PRNG(\text{SEEDOTS}_j)$.

My question: How is possible generate the same key for public key generation and during the signing phase, for each one-time signature key, if $x_i$ is random (by definition of $\text{PRNG}$)?

-
Your post doesn't have the $\$$symbols, and I can't quite tell where they should be.$\hspace{1.05 in}\$ –  Ricky Demer Jul 8 '13 at 0:33
@RickyDemer I edit my question –  juaninf Jul 8 '13 at 0:43