A quantum dissipation theory is constructed with the system-bath interaction being treated rigorously at the second-order cumulant level for both reduced dynamics and initial canonical boundary condition. The theory is valid for arbitrary bath correlation functions and time-dependent external driving fields, and satisfies correlated detailed-balance relation at any temperatures. The general formulation assumes a particularly simple form in driven Brownian oscillator systems in which the correlated driving-dissipation effects can be accounted for exactly in terms of local-field correction. Remarks on a class of widely used phenomenological quantum master equations that neglects the bath dispersion-induced dissipation are also made in contact with the present theory.