I have a question regarding Lemma 7.2 on page 86. As I read the proof of the lemma, it says "The class $\Psi(\alpha)$ is represented by any oriented disk $D^\lambda$ which intersects $S_R$ in one point $x$, transversely, with intersection number $S_R \cdot D^\lambda = 1$."

I am not quite sure why $D^\lambda$ has to intersects with $S_R$ in a single point transversely with the intersection number $+1$. This has to happen because $D^\lambda$ is an orientation generator?