We systematically investigate the mass spectrum, spatial configuration and magnetic moment of the ground and $P$-wave states $[cu][\bar{c}\bar{s}]$ with various color-spin configurations in the multiquark color flux-tube model. Numerical results indicate that the state $Z_{cs}(4000)^+$ can be described as the compact state $[cu][\bar{c}\bar{s}]$ with $1^3S_1$. Its main color-spin configuration is $[cu]^{1}_{\mathbf{6}_c} [\bar{c}\bar{s}]^{1}_{\bar{\mathbf{6}}_c}$ and its magnetic moment is 0.73 $\mu_N$. The state $Z_{cs}(4220)^+$ can be depicted as the compact state $[cu][\bar{c}\bar{s}]$ with $1^1P_1$ (or $1^3P_1$). Its main color-spin configuration is $[cu]^{0}_{\bar{\mathbf{3}}_c}[\bar{c}\bar{s}]^{0}_{\mathbf{3}_c}$ (or $[cu]^{0}_{\bar{\mathbf{3}}_c}[\bar{c}\bar{s}]^{1}_{\mathbf{3}_c}$) and its magnetic moment is 0.12 $\mu_N$ (or 0.64 $\mu_N$). The physical state should be the mixture of these two different color-spin configurations and deserves further investigation. In addition, we also predict the properties of the states $[cu][\bar{c}\bar{s}]$ with other quantum numbers in the model.