This can be done in the Triggers section of the destination pipeline stage. For example if you move a lead to 1st msg sent, the triggers on the 1st msg sent stage can be set to automatically set a card color and follow up date. Since automations normally move leads to another stage, the destination stage is the one that sets these parameters.

If this doesn't fulfil what you're looking to do please give me info about the specific use case so we can understand what the logic is.