Hi finishthepint,
This is called the output glitch. You are correct in stating that the more bits that transition during a DAC update, the larger the spike. We have specified this typical performance in Figure 26 of the AD5725 Data Sheet.
As for the reduction of the glitch, you could make an RC filter at the output. Take note that when you implement the RC filter, the DAC will have longer settling time at the output.