  We update the study of the total Psi and Upsilon production cross section in
proton-proton collisions at RHIC energies using the QCD-based Color-Singlet
(CS) Model, including next-to-leading order partonic matrix elements. We also
include charm-quark initiated processes which appear at leading order in
alpha_s, but which have so far been overlooked in such studies. Contrary to
earlier claims, we show that the CS yield is consistent with measurements over
a broad range of J/Psi rapidities. We also find that charm-quark initiated
processes, including both intrinsic and sea-like charm components, typically
contribute at least 20% of the direct J/Psi yield, improving the agreement with
data both for the integrated cross section and its rapidity dependence. The key
signature for such processes is the observation of a charm-quark jet opposite
in azimuthal angle phi to the detected J/Psi. Our results have impact on the
proper interpretation of heavy-quarkonium production in heavy-ion collisions
and its use as a probe for the quark-gluon plasma.
