The strong monodromy conjecture for tuples of polynomials

Let $F=(f_1,\ldots,f_p)$ be a tuple of polynomials $f_i\in\mathbb{C}[x_1,\ldots,x_n]$. Let $Z_F^{top}(s_1,\ldots,s_p)$ be the topological zeta function of $F$, with polar locus $\mathcal{P}(Z_F^{top})$. Let $B_F$ be the Bernstein–Sato ideal and let $Z(B_F)\subset\mathbb{C}^p$ be its zero locus. Strong monodromy conjecture. The inclusion

$$\mathcal{P}(Z_F^{top})\subset Z(B_F)$$

should hold. This strengthens the monodromy conjecture by relating the poles of the topological zeta function directly to the Bernstein–Sato ideal; the supplied text does not state its resolution.