At what age should a teen's tonsils shrink away?

Not clear. Tonsils do not necessarily "automatically" go away as children get older. The adenoids which are similar to the tonsils usually do regress during the teenage years. If the tonsils are large and obstructing and causing significant symptoms waiting until they "go down" is not reasonable.
Depends. They can get smaller during 20s to adulthood. They may never get smaller. Various factors play into tonsillar size, including acute infection, chronic infection, allergy and heredity (family history). If there are more than 3 infections a year over several years its worth considering removal especially if complications arise. If the tonsils are different size then removal is also considered.
Teenage years. At birth, your tonsils and adenoids (t&a) are small and your immune system is immature. Your t&a are immunological structures and make antibodies to pathogens, like bacteria and viruses; so as you grow, they grow and enlarge, doing their job. Our immune system is relatively mature at 5 to 7 years of age, when the t&a peak in size. They then usually shrink to become small again by preteen/teenager.