If I understood your question correctly, the answer is yes. More precisely, the following statement should hold:
If $X$ is a closed manifold of positive sectional curvature and $Y\subset X$ is a codimension one totally geodesic submanifold that disconnects $X$, then $X$ is homeomorphic to a sphere.
This follows, as you say, from the Soul Argument of Perelman (see, e.g., Section 6 of Perelman's notes).
More precisely, denote by $C_1$ and $C_2$ the closure of the two connected components of $X\setminus Y$. These are positively curved compact Alexandrov spaces with boundary $Y$. On each of them, since the curvature is positive, the distance function to the boundary is concave. Therefore, the set of points at maximal distance (the soul) consists of a unique point. This implies that each $C_i$ is homeomorphic to a disk, hence $X=C_1\cup_{Y} C_2$ is a twisted sphere.