Yes, as far as Buddhism goes, they are alive somewhere else. They might be a four year old kid next door. We don't know. So wherever they are, we wish them well.
As far as when I do it concerning people who are dead, I add a little phrase at the beginning of my wish. For me personally I don't know if rebirth's true, so what I say at the beginning of my wish is, "If rebirth is true, may so and so, so and so", and I use exactly the same phrase that I would use for people who are still living. I add just a little bit in the beginning because this is being honest to oneself and, if rebirth is true, then I still give them that generous wish wherever they are.
When you think of death and rebirth and this sort of stuff, you really only have to think about rooms in a big house. You are stuck in one room, then you went out a door and you are in another room. It's as simple as that. Let's say right here, we are in a room and we have no idea right now if that other building is there or not. We have no idea. They are in a separate room, we are here, they are there. When we get up and go out this door, you are not sure, you have this bit of awareness that, yes, one of these days you are going to die where you are.
Now, it's very unusual, about a month ago it was one of the very few times when a Thai made a joke which we understood. Our Thai is pretty good and his English was pretty good, so it was a combination of Thai and English. He simply said, "You are going to die in one week." He had been talking about his mother's psychic phenomena and things prior to that, and I say, "Are you sure?" He responded, "Yup, you are going to die in one week." I say, "So, okay, tell me, how do you know?" He says, "It's easy. One week, it has Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, you are going to die in one week." Okay, we are going to die whether it's a Sunday or Monday or Tuesday, and we are going to die in one place, too. That's helpful to know. You are going to die in one place. You don't know whether you are going to die sitting here or out there walking but you are definitely going to die somewhere in one place.
So if we think about different rooms, we can think about dying. It's very helpful to consider, why can't the other beings - as we were talking about the other beings being dead - simply exist, but they are in a different type of room, in a different place within this whole universe? On top of this you might like to know that Buddhism does teach that if you have strong Kammic connections, such as the legend of the Buddha with his wife, Yasadhara for 500 lifetimes, you will see the other person again in a future life.