When I say two time dimensions, I mean two timelike dimensions.
When I say two time dimensions, I mean two timelike dimensions. In the usual scheme of general relativity we have one timelike dimension which we usually equate with time because they "act like" time. The other dimensions are spacelike because they "act like" space. If you have two timelike dimensions, that means that you can do things like move in a circle in time (basically violate causality). Now, the AdS means that this is a surface that is embedded in a universe with two timelike dimensions. Think of a sphere that is embedded in an ordinary volume (what we would call Euclidean). Imagine a universe exists on its surface. That is the idea here. The AdS is kind of like a sphere that is embedded in a volume with two timelike dimensions. It doesn't look or act like a sphere though. It actually is more cylindrical because the two time dimensions make up a circle and then the space dimensions are perpendicular to that as in a cylinder. In deSitter you only have the one time and so no causality violations. You can still have multiple temporal dimensions because temporal dimensions can be spacelike or timelike.