Reactions of neutralization
\begin{align}
\ce{HA(aq) + OH-(aq) &-> A-(aq) + H2O} \tag{R1}\\
\ce{A-(aq) + H+(aq) &-> HA(aq)}\tag{R2}\\
\ce{H+(aq) + OH-(aq) &-> H2O} \tag{R3}
\end{align}
dissociation
\begin{align}
\ce{HA(aq) &-> A-(aq) + H+(aq)} \tag{R4}\\
\ce{H2O &-> H+(aq) + OH-(aq)} \tag{R5}
\end{align}
and hydrolysis
$$\ce{A-(aq) + H2O -> HA(aq) + OH-(aq)} \tag{R6}$$
always occur simultaneously.
Reactions can be rewritten as the half number of equilibrium reactions instead:
\begin{align}
\ce{A-(aq) + H2O &<=> HA(aq) + OH-(aq)} &K_\mathrm{b} \tag{R7} \\
\ce{ HA(aq) &<=> A-(aq) + H+(aq)} &K_\mathrm{a} \tag{R8}\\
\ce{H2O &<=> H+(aq) + OH-(aq)} &K_\mathrm{w} \tag{R9}
\end{align}
bound by the equation of the equilibrium constant dependency
$$K_\mathrm{a} \cdot K_\mathrm{b} = K_\mathrm{w}$$
Which reaction direction dominates depends on concentration of involved species and respective dissociation constants. As for all acid-base reactions, equilibrium is established very fast by approaching it from either left either right side of the reaction. At the equilibrium, the rates of respective forward and backward reactions are equal and the net reaction rates are zero.
The same occurs in respective modifications for cases of strong acids and weak bases, or weak acids and weak bases.