Do the inside of tangerine peels whiten teeth like the inside of orange peels?

No. Tangerines are very acidic and placing these on enamel for long periods of time will only damage your enamel! stick to the professional or over the counter whitening that have well documented success!
Short term fix. The acids in both peels will dissolve away stain as they are dissolving your tooth enamel. Not a good idea...
Supposedly, yes. I've never tried it or known anyone who tried it, but supposedly, yes, tangerines and oranges have this effect in common. Two methods. You can rub the peel on each individual tooth. Or you can dry the tangerine peel and grind it into powder, and then use the mixture of the powder with your toothpaste when you brush your teeth.