Alundra is able to keep all treasures and money he finds in dreams.
Because, the big bad evil thing that is coming through is making dreams real, and they affect real life. More than one character dies from the dreams. So, anything Alundra picks up would be real outside the dreams, too.
I think the presence of a Dreamwalker creates a metaphysical bridge over which things can become reified. Nothing is shown to emerge from dreams without a Dreamwalker involved — even the wolf transformations are technically contained within the victim, even though it manifests in reality. Note, for example, the implied fact that Melzas couldn't send the Murgg through the twins' dream until Alundra entered it. And if that explanation doesn't satisfy you, we can just chalk it up to the inventory being a special exception. Alundra can take items in and, more importantly, consume them, so it stands to reason that he can take them out, too. The really weird question isn't how, anyway. It's why, as in, "why the hell are there Gilded Falcons inside people's heads?"