Two embedded symplectic spheres with zero square in a symplectic $4$-manifold I am aware that the following result is a classical one (by now). But I am not able to understand who proved it. What should be a proper reference to this statement?
Theorem. Let $M^4$ be a compact symplectic manifold with $\pi_1\ne 0$ and let $S_1$ and $S_2$ be two symplectic spheres embedded in it with $S_1^2=S_2^2=0$. Then $S_1$ and $S_2$ are symplectically isotopic in $M^4$. 
In other words, is there an article/book (say pre 2000) claiming that any two symplectic spheres with zero self-intersection in an irrational ruled (non-minimal) surface are symplectically isotopic?
 A: It looks indeed that this question is not as classical is it sounds, so let me provide a  2010 reference to a more general statement, at least to show that there is a reference. This is Proposition 3.2 in the following paper:
https://arxiv.org/abs/1012.4146
A: Partial attempt of answer if $M$ is minimal. Since $S_1$ is an embedded sphere, there exists a diffeomorphism $e_i:M(J,S_i)\times_GS^2\rightarrow M, i=1,2$ (see 1) induced by the evaluation map.
Since $\pi_1(M)$ is not trivial, the base of the fibration is a surface of genus $>0$. The Serre exact sequence of the fibration shows that $\pi_2(M)$ is generated by $\pi_2(S_1)=\pi_1(S_2)$ and the Hurewicz morphism implies that the classes $[S_1]$ of $[S_2]$ are equal in $H_2(M)$.  We deduce that $[S_1].[S_2]=0$ and $S_1\cap S_2$ is empty.  This implies that $S_2$ coincide with the  fibre of $e_1$ which contains one of its point. We can also say that since $[S_1]=[S_2]$, $S_2$ is realized by $e_1$.  We deduce that  there is a symplectic isotopy between $S_1$ and $S_2$.
Introduction to symplectic topology p. 185 vi) McDuff and Solomon.
