The actions are defined in the Kashiwara's paper: [On crystal bases of the Q-analogue of universal enveloping algebras](https://projecteuclid.org/euclid.dmj/1077295931) 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*}
$v \in \ker f_i \cap M_{\mu}$, $0 \leq n \leq - \langle h_i, \mu \rangle$.