If $\pi: E \rightarrow M$ is a vector bundle, what does it mean that $E^X$ is equal to $M$ such that $E^X \subset E$?

Question

I've come across this statement:

Let $G$ be a compact Lie group with Lie algebra $\mathfrak{g}$. Let $\pi: E \rightarrow M$ be a G-equivariant vector bundle. Suppose that there exists $X \in \mathfrak{g}$ such that $E^X =M$: the vector field on $E$ induced by $X$ vanishes exactly on $M$.

My question is :

what does it mean that $E^X$ which is a subset of $E$ is equal to $M$ which might be different from $E$ ?