  We investigate the single transverse-spin asymmetry with a $\sin
(\phi_h-\phi_S)$ modulation in the charged Kaon produced and in $\Lambda$
hyperon produced SIDIS process within the theoretical framework of transverse
momentum dependent (TMD) factorization at the next-to-leading-logarithmic
order. The asymmetry is contributed by the convolution of Sivers function and
the unpolarized fragmentation function $D_1$ for the produced hadron. The
parametrization for the proton Qiu-Sterman function, which is closely related
to the Sivers function, is adopted to numerically estimate the Sivers asymmetry
at the kinematical region of Electron Ion Collider (EIC) and Electron Ion
Collider in China (EicC). The TMD evolution of the TMD parton distribution
functions are considered by employing the nonperturbative Sudakov form factor.
It is found that the predicted Sivers asymmetries $A_{UT}^{\sin
(\phi_h-\phi_S)}$ as functions of $x$, $z$ and $P_{hT}$ are sizable at the
kinematical configurations of both EIC and EicC. The strange constituent of the
produced charged Kaon and $\Lambda$ hyperon in the final state can be a
promising probe of the sea quark Sivers function as well as the flavor
dependence in the proton target. Therefore, it is important to utilize the
future EIC facilities to constrain the sea quark distribution functions as well
as the validity of the generalized universality of the Sivers function.
