Case fields?

They will be constraints on the filter. 

Hi Amber,

To clarify what Cathal said, when you've set up the case in your Custom Object sync, you'll need to use the Has Case filter, and then your synched fields will appear as constraint on this filter.

So, I can only get this with a filter, not a trigger? Any suggestions on something I can use for the trigger? I would prefer not to set this up as a batch campaign.

You can set this up as a trigger, you just need to ensure that the fields are available as trigger constraints in your Object sync menu.  The fields for triggers and filters are selected separately.

Admin - > Salesforce -> Object sync
Select the case object
Then click edit visible fields and you can enable each field as a constraint for the added to case trigger.
(The object can't be in use when you try this so you will have to delete and case filters/triggers that you have in campaigns , a personal peeve of mine)