There's only five different teens per generation...so if you care for it the same you'll probably get the same one. But if you wait until the matchmaker comes and don't let your tama die you'll be guranteed a different teen for the next generation.
I wouldn't say it's particularly strange. Since all the characters you get depend on how well you take care of it.... I would suggest that when you get Puchitchi or Shiropuchitchi you take excellent care of it until it's teen years. If that doesn't break the Nikatchi spell.... I'll be at a loss!