The actions are defined in the Kashiwara's paper: On crystal bases of the Q-analogue of universal enveloping algebras in (2.2.5).
Let $M$ be an integrable $U_q(\mathfrak{g})$-module. Then \begin{align*} M = \oplus_{0 \leq n \leq -\langle H_i, \mu \rangle} e_i^{(n)} (\ker f_i \cap M_{\mu}), \end{align*} where $M_{\mu} = \{u \in M: h\cdot u = \langle h, \mu \rangle u, \forall \ h \in P^* \}$, $P$ is the weight lattice of $\mathfrak{g}$.
The actions of $\tilde{e}_i$ and $\tilde{f}_i$ on $M$ are given by \begin{align*} & \tilde{e}_i(e_i^{(n)} v) = e_i^{(n+1)}v, \\ & \tilde{f}_i(e_i^{(n)} v) = e_i^{(n-1)}v, \end{align*} $v \in \ker f_i \cap M_{\mu}$, $0 \leq n \leq - \langle h_i, \mu \rangle$.