Recently, the CDF and D0 collaborations measured indirect CP violation in B(s)(0) -> J/psi phi and found a hint of a signal. If taken at face value, this can be interpreted as a nonzero phase of B(s)(0)-($) over bar (0)(s) mixing (beta s), in disagreement with the standard model, which predicts that beta(s) similar or equal to 0. In this paper, we argue that this analysis may be incomplete. In particular, there can be new physics (NP) in the (b) over bar -> (s) over barc (c) over bar decay. If so, the value of beta(s) is different than for the case in which NP is assumed to be present only in the mixing. We have examined several models of NP and found that, indeed, there can be significant contributions to the decay. These effects are consistent with measurements in B -> J/psi K* and B(d)(0) -> J/psi K(S). Due to the NP in the decay, polarization-dependent indirect CP asymmetries and triple-product asymmetries are predicted in B(s)(0) -> J/psi phi.