  Long-range correlations for pairs of charged particles with two-particle
angular correlations are studied in $pp$ at ${\sqrt{{\textit s}}}=13$~TeV with
various Monte Carlo generators. The correlation functions are constructed as
functions of relative azimuthal angle $\Delta\varphi$ and pseudorapidity
separation $\Delta\eta$ for pairs of different particle species with the
identified hadrons such as $\pi$, $K$, $p$, and $\Lambda$ in wide $\Delta\eta$
ranges. Fourier coefficients are extracted for the long-range correlations in
several -multiplicity classes using a low-multiplicity template fit method. The
method allows to subtract the enhanced away-side jet fragments in
high-multiplicity with respect to low-multiplicity events. However, we found
that due to a kinematic bias on jets and differing model implementation of flow
and jet components, subtracting the non-flow contamination in small systems can
bias the results. It is found that PYTHIA8 Default model where the presence of
the collective flow is not expected but the bias results in very large flow.
Also extracting flow signal from the EPOS4 and PYTHIA8 String Shoving models is
not possible because of flow signal introduced in the low-multiplicity events.
Only AMPT String Melting model among studied model calculations is free from
this bias, and shows a mass ordering at low $p_{\mathrm{T}}$ and particle type
grouping in the intermediate $p_{\mathrm{T}}$ range. This feature has first
found in large systems but the mass ordering in small systems is different from
what is observed in the large collision systems.
