What alignment is the awakened animal/construct? I assume the same as the caster.
I was unable to find a concrete answer for Awaken in its description, but
Its alignment is determined by the GM, but is usually within one step of its creator’s alignment.
The alignment of an awakened animal or tree wouldn't change, at least until the creature acted to differentiate itself. Awaken doesn't say anything about a creature's personality other than that it will be friendly to the caster and perform tasks for them, which is something of a magical compulsion. So it'd be subject to the same process that other characters are subject to with respect to alignment drift. If you awaken a fir tree and it happens to be an omnicidal maniac, it'll probably drift toward chaotic evil over time.
I imagine CE is the default alignment for sandbox trees.