This was a tough question. How long did it take for Lucas and Eli to understand that our home was their home?
During the first year home I don't think they truly understood the permanence. Permanence had to be proven. They should have come with signs saying, "Prove It To Me!" They would go through phases, that we'd call "check in with the Philippines" where they'd ask if they decided to go back to the Philippines would that be ok with us, would we take them to visit (they were always careful to make sure we understood it was for the purpose of visiting only).
Later on it became talk of when they grew up that they want to take their children to see the Philippines. That's the phase we are at right now.
The other big event that helped to solidify home as theirs was when they each got their own room. For us, it was a necessity as they were going to kill one another if they stayed in the same room. Their initial tight bond loosened and they became their own individuals with definite likes, dislikes and (shall we say) levels of neatness. Lucas being the neater and Eli being "if it hits the doorway it is put away" type of kid. Separate rooms and their input into the room style gave them ownership and pride. It was a good move, a little hard on me and my sense of what looked good but hey they like it.
So ultimately I'd say they felt like this was home consistently after that first year. The pressing issues of the first year's adjustments had settled down and they were able to settle in. When we were in Florida on vacation this summer we'd only been gone from home for 3 hours when they started checking on when we'd be home again, who was taking care of home and how much they missed it. I think they've settled in for the long haul.