Fluid antenna multiple access (FAMA) enables each user to rapidly switch among several closely spaced ports and select the strongest received signal. Although this mechanism offers micro-scale spatial diversity, its behavior in multiuser downlink systems with spatial correlation and linear precoding is not well understood. This paper develops a unified analytical framework for the multiple-input single-output (MISO) downlink with FAMA users served via maximum ratio transmission (MRT) or zero-forcing (ZF). We show that the per-port signal-to-interference ratio (SIR) follows a Beta-prime distribution with parameters \((M_{\mathrm{eff}},L)\), where \(M_{\mathrm{eff}}=M\) under MRT and \(M_{\mathrm{eff}}=M-U+1\) under ZF, and derive closed-form finite-sum cumulative distribution functions (CDFs) for both cases. We further provide the first analytical characterization of cross-port SIR correlation. \textcolor{black}{Furthermore, we derive rigorous outage probability bounds that tightly bracket the exact performance and become exact in the limiting cases of fully correlated and independent ports.} Asymptotic analyses reveal the fundamental diversity orders and tail behavior for each precoder. Numerical results confirm the accuracy of the SIR distributions, correlation model, and outage bounds, and show that MRT achieves weaker port correlation and larger selection gains than ZF when the base station (BS) has ample spatial degrees of freedom. The framework offers explicit guidelines for port configuration and precoder selection in practical FAMA systems.