Bouquet conjecture for splitting of isolated singularities

Let $(X_0,f_0)$ be an isolated singularity, and consider a one-parameter deformation $(X_t,f_t)$ in which the singularity splits into isolated singularities. Let the Milnor fibre of $(X_0,f_0)$ and the Milnor fibres of the resulting isolated singularities be understood in the usual sense.

Bouquet conjecture. The Milnor fibre of $(X_0,f_0)$ is homotopy equivalent to the bouquet of the Milnor fibres of the isolated singularities into which it splits.

This predicts that splitting decomposes the topology of the original Milnor fibre as a bouquet of the fibres of the singularities produced by the deformation. The source presents this as a question and gives no resolution.