Which version do you have?
Here's the information for the latest model (the V5):
baby + 1 hour = toddler
toddler + 48 hours (2 days) = teen
teen + 48 hours = adult
adult + 48 hours = now can mate (now can use the dating show.) They become parents when they mate & have babies.
Note: The above are unpaused times.
The Gen counter shows the generation of the current characters on your Tamagotchi toy.
For the V1 through V4.5 the Gen counter goes up when the parents leave the babies in your care. This occurs the second day after they mate.
However, for the V5 one of your Gen 1 characters will stay as a parent while you're raising the Gen 2 babies. It's not until the Gen 2 babies have become adults and one of them has mated that the last Gen 1 character leaves.
So, let's say it takes a week to go through a generation on the V5. Your Gen counter should progress like this.
Week 0 (start): 3 orphan eggs, Gen 1.
Week 1: 3 adults. Mate one. You now have two parents, and some babies. Still Gen 1.
Week 2: last week's babies are now adults. Mate one. You now have two new parents and some new babies. Now Gen 2.
Week 3: those "new" babies are now adults. Mate one. You now have two new parents and some new babies. Now Gen 3.