How Does a Buck Converter Maintain a Constant Voltage?
What changes in the buck converter to meet the increase current demand?
The duty cycle of the PWM signal (which controls the switching element) is changed such that the output voltage remains constant.

Picture found here.
In this picture, the PWM signal is marked k(t).
The error signal \$V_e\$ ( = \$V_{ref} - V_o)\$ is amplified and then used to influence the PWM signal.
What the actual shape of the current through the inductor looks like depends on the load current. Your drawing might be correct for many of those situations.