<p>The ${\mathfrak{sl}}_3$ colored Jones polynomial $J_{\lambda }^{\mathfrak{s}{\mathfrak{l}}_3}(L)$ is obtained by coloring the link components with two-row Young diagram $\lambda$. Although it is difficult to compute $J_{\lambda }^{\mathfrak{s}{\mathfrak{l}}_3}(L)$ in general, we can calculate it by using Kuperberg $A_2$ skein relation. In this paper, we show some formulas for twisted two strands colored by one-row Young diagram in $A_2$ web space and compute $J_{(n,0)}^{\mathfrak{s}{\mathfrak{l}}_3}(T(2,2m))$ for an oriented $(2,2m)$-torus link. These explicit formulas derives the ${\mathfrak{sl}}_3$ tail of $T(2,2m)$. They also give explicit descriptions of the ${\mathfrak{sl}}_3$ false theta series with one-row coloring because the ${\mathfrak{sl}}_2$ tail of $T(2,2m)$ is known as the false theta series.</p>