Ashley,
I’m not really using the gravity forms, so not sure about the tag refreshing, but I do know that even inside Infusionsoft campaign builder, new tags that I create seem to take a little while before I can pull them up in a search inside of CB.
As far as applying a tag that triggers a campaign, I use legacy action sets for things like this. Not sure if Gravity allows you to trigger an action set, but if so, just make the action set under Marketing> Settings> Action Sets> Add Action Set> (Action) Apply a Tag.
Also, if you’re new to Campaign Builder and using tags as triggers, remember that if there’s a chance that a contact might need to come back through that campaign again in the future, make sure you make your first step in the Campaign Follow-Up sequence to REMOVE the trigger tag. We use tags like ‘light switches’ in Campaign Builder so they can be triggered over and over.