You're not horrible but a week really isn't much time to give anyone a chance especially if you've knowingly jumped from a throw shit out the door as quickly as possible and see if it works culture to a more "considered" slower paced approach and feels a little unfair on the company who've taken a chance on hiring you.

If you're willing to hang around and perhaps try to bring some of your ideas or process improvements to the table then if it were my company I'd prefer you just went asap and I could get someone who was a better fit and no hard feelings as the hiring process doesn't seem to have flagged that you might not be right for the workflow/process of the new place.