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The vapor-liquid critical behavior of intrinsically asymmetric fluids isstudied in finite systems of linear dimensions, $L$, focusing on periodicboundary conditions, as appropriate for simulations. The recently propounded``complete'' thermodynamic $(L\to\infty)$ scaling theory incorporating pressuremixing in the scaling fields as well as corrections to scaling${[arXiv:cond-mat/0212145]}$, is extended to finite $L$, initially in a grandcanonical representation. The theory allows for a Yang-Yang anomaly in which,when $L\to\infty$, the second temperature derivative,$(d^{2}\mu_{\sigma}/dT^{2})$, of the chemical potential along the phaseboundary, $\mu_{\sigma}(T)$, diverges when $T\to\Tc -$. The finite-sizebehavior of various special {\em critical loci} in the temperature-density or$(T,\rho)$ plane, in particular, the $k$-inflection susceptibility loci and the$Q$-maximal loci -- derived from $Q_{L}(T,<\rho>_{L}) \equiv < m^{2}>^{2}_{L}/<m^{4}>_{L}$ where $m \equiv \rho - <\rho>_{L}$ -- is carefully elucidated andshown to be of value in estimating $\Tc$ and $\rhoc$. Concrete illustrationsare presented for the hard-core square-well fluid and for the restrictedprimitive model electrolyte including an estimate of the correlation exponent$\nu$ that confirms Ising-type character. The treatment is extended to thecanonical representation where further complications appear.Comment: 23 pages in the two-column format (including 13 figures) This is Part  II of the previous paper [arXiv:cond-mat/0212145

Asymmetric fluid criticality. II. Finite-size scaling for simulations