Cubase has great automation features and a solid quantization scheme in general (midi, audio, event snapping, etc). But… It’s odd that there is no menu option to quantize selected automation events. I hope they change that. I did find this Project Logical Editor workflow from Vic_France (longtime member of Steinberg’s forum).

Cubase PLE Preset

You can reference the image to see the needed arguments for the editor.

Here are the settings you DO NOT change…

Media Type is – This makes “automation” the target of the operation.
Property:Property is set – This sets up the test to quantize only the events you have selected.
Position:Add – This makes the value adjusted PPQ

The only one you DO need to change is…

Position:Round by – This is the values that creates the new position. If you want to round to 1/8 or 1/4 or triplet 8ths, you’ll need to changes this value.

PPQ (parts per quarter) is just a part of how MIDI works. This setting can be changed. Commonly in Cubase and other programs we use a 480 PPQ based system. That means a full measure is 1920 PPQ. Some math will give you all the other rhythmic values.