If the tinnitus is Otic in nature it is difficult to effect it. If it is somatically modulatable then you have a chance to effect it. I test to see if I can influence it with neck, jaw active and resisted testing. You are correct you should correct upper cervical joint restrictions, specifically C2-3. DN treatment should focus on SCM, suboccipitals, all trigeminally innervated structures with specific emphasis on Medial Pterygoid. You should see improvement in the somatically generated noise relatively quickly. Many times it is a combo of otic and somatic so the patient will report a reduction in symptoms but not a full resolution.
Hope that helps