Deeper levels of tundra islands should count as individual islands in a pet's research points, you have to use a portal cell to get to one and it is technically a "new island". 

I had my Gryphon explore lots of Tundra but they only have 28 islands explored in their research points.

Going deeper into an island isn't the same as going to a different island. You do use an item to get to the deeper levels, but energy is not spent traveling to deeper levels of the same island. The research points are given for going to islands, which is done by expending energy. It makes sense that going deeper into the same island does not count as being a new island.

Yes, just like Sunset mentioned already, it's a different resource. This achievement supposes that a pet goes through the portal in your manor and spends energy points and an portal memory entry (unless it's a free Watchman's visit) to reach its destination and see something new. Tundra already provides a nice opportunity to speed up leveling and stock up on some of the resources. This change is a small one, but it would add up to the imbalance.