Migration on WikiTree (for categories and the migration sticker) have been defined as the movement from one country to another with the intention of settling permanently in the new location.
Based on the information given, I would say that:
Rev Joseph Berry and his wife Agnes Osborn were both born in England, migrated to New Zealand, married in New Zealand in 1870 and had a total of 14 children.
Rev Joseph Berry and his wife Agnes Osborn obviously qualify for England > New Zealand migration.
They were on one of several trips overseas when Agnes gave birth to a daughter, Constance, in 1879 in Germany.
1) Does Constance qualify for a migration sticker from Germany to New Zealand?
2) Does she qualify for a migration sticker from New Zealand to Australia?
1) In this instance, I would say that Constance was not involved in a migration event (Germany > New Zealand), but rather she was just born abroad.
2) Most definitely this would qualify, as her primary residence was in New Zealand and they uprooted and moved to Australia.
Agnes also gave birth to a son, Bernard, in 1881, at sea, three days before arriving back at Auckland New Zealand.
The family migrated to Australia in 1893.
3) Does Bernard qualify for a migration sticker from New Zealand to Australia?
3) Most definitely this would qualify, as his primary residence was in New Zealand and they uprooted and moved to Australia.
Note: Births and deaths at sea (on a ship) can be complicated by the fact that the event could fall under the laws and jurisdiction of the state in which the craft is registered.
For example, if Bernard was born at sea on a German registered vessel, it is very possible that he would be considered to have been born in Germany. This would still not officially qualify for a migration event my mind, since there was no permanent residence, or intent to move to a new country - the cards just fell in a peculiar way.