  The charmonium-like exotic states $Y(4230)$ and the less known $Y(4320)$,
produced in $e^+e^-$ collisions, are sources of positive parity exotic hadrons
in association with photons or pseudoscalar mesons. We analyze the radiative
and pion decay channels in the compact tetraquark scheme, with a method that
proves to work equally well in the most studied $D^*\to \gamma/\pi+D$ decays.
The decay of the vector $Y$ into a pion and a $Z_c$ state requires a flip of
charge conjugation and isospin that is described appropriately in the formalism
used. Rates however are found to depend on the fifth power of pion momentum
which would make the final states $\pi Z_c(4020)$ strongly suppressed with
respect to $\pi Z_c(3900)$. The agreement with BES III data would be improved
considering the $\pi Z_c(4020)$ events to be fed by the tail of the $Y(4320)$
resonance under the $Y(4230)$. These results should renovate the interest in
further clarifying the emerging experimental picture in this mass region.
