Cell size is specific to each species and impacts their ability to function. While various phenomenological models for cell size regulation have been proposed, recent work in bacteria have demonstrated an adder mechanism, in which a cell increments its size by a constant amount between each division. However, the coupling between cell size, shape and constriction, remain poorly understood. Here, we investigate size control and the cell cycle dependence of bacterial growth, using multigenerational cell growth and shape data for single Caulobacter crescentus cells. Our analysis reveals a biphasic growth mechanism: a relative timer phase before constriction where cell growth is correlated to its initial size, followed by a pure adder phase during constriction. Cell wall labeling measurements reinforce this biphasic behavior: a crossover from uniform lateral growth to localized septal growth is observed. We develop a mathematical model that quantitatively explains this mixer mechanism for size control.