  A large anti-correlation signal between elliptic flow $v_2$ and average
transverse momentum $[p_{\mathrm{T}}]$ was recently measured in small collision
systems, consistent with a final-state hydrodynamic response to the initial
geometry. This negative $v_2$-$[p_{\mathrm{T}}]$ correlation was predicted to
change to positive correlation for events with very small charged particle
multiplicity $N_{\mathrm{ch}}$ due to initial-state momentum anisotropies of
the gluon saturation effects. However, the role of non-flow correlations is
expected to be important in these systems, which is not yet studied. We
estimate the non-flow effects in $pp$, $p$Pb and peripheral PbPb collisions
using {\tt Pythia} and {\tt Hijing} models, and compare them with the
experimental data. We show that the non-flow effects are largely suppressed
using the rapidity-separated subevent cumulant method (details of the cumulant
framework are also provided). The magnitude of the residual non-flow is much
less than the experimental observation in the higher $N_{\mathrm{ch}}$ region,
supporting the final-state response interpretation. In the very low
$N_{\mathrm{ch}}$ region, however, the sign and magnitude of the residual
non-flow depend on the model details. Therefore, it is unclear at this moment
whether the sign change of $v_2$-$[p_{\mathrm{T}}]$ can serve as evidence for
initial state momentum anisotropies predicted by the gluon saturation.
