While there is a Gen (generation) counter on the Osutchi-Mesutchi, except during the first generation, the Gen number is not related to the characters you can get.
TMP = TaMagotchi Power. There are four TMP levels. The TMP level determines which characters you can raise. It's probably the TMP level groupings of characters you're seeing, and confusing the TMP level with the Gen counter.
At Gen 1, TMP is also 1. If you take good care of your characters, their children may get a higher TMP level than the parents. (Note: If you breed a low-TMP adult with a high-TMP adult, the children's TMP level may be 1 above the low-TMP adult's TMP level.) After several generations of good care, you may achieve TMP level 4 characters. If you take very good care of your TMP level 4 characters, but then don't breed them, they may turn into oldies. (Note: oldies can't breed.) If you breed two TMP level 4 characters, I believe their children could be TMP level 4 or TMP level 3 characters.
Note: The Osutchi-Mesutchi doesn't have a download feature. When the batteries run out, all data is lost. (Also, the reset button on the back is a complete reset.) Make sure you install fresh batteries before you hatch them.
