To a given a Laurent polynomial $f$ over the field of Puiseux seris with parameter $t$, $f \in \mathbb{C} \lbrace\lbrace t \rbrace\rbrace[z_1^{\pm1},...,z_n^{\pm 1}]$, one can associate the hypersurface $$V_{f} =\overline{\lbrace(t_1,...,t_n ) \in (\mathbb{C} \lbrace\lbrace t \rbrace\rbrace)^n : f(t_1,...t_n)=0 \rbrace }$$.

Then, what it would mean if two of such hypersurfaces are transversal(in terms of generic $t$ and varieties over $\mathbb{C}$)?

If for an ideal $I=\; < g_t,h_t>\; \subset \mathbb{C} \lbrace\lbrace t \rbrace\rbrace[z_1^{\pm1},...,z_n^{\pm 1}]$,

$$V(I)= \overline{\lbrace(t_1,...,t_n ) \in (\mathbb{C} \lbrace\lbrace t \rbrace\rbrace)^n : f(t_1,...t_n)=0 , \forall f \in I \rbrace } $$ is irreducible, does imply the transversality of $V_f$ and $V_g$ over $\mathbb{C}$ for generic parameter $t \in \mathbb{R}$?