Intonation as you move away from the nut is controlled by tension, all other things being equal. The strings of different gages are rarely under exactly the same tension - in fact with most sets the thinner strings are intentionally under higher tension to balance the volume across the strings. On most electric guitars you can actually move the saddle back and forth until you get it "set up" so that each string rings at exactly the right pitch at the 12th (or some people use the 15th) fret when the open string is tuned correctly.
Most acoustic guitars don't have movable saddles but do have a compensated bridge, where a certain amount of compensation is built into the shape at the top. Very few ukuleles do. Kiwaya ukes have compensated saddles, but those were the only production ukes I know of. I've compensated the saddles on a couple of my ukes.
For reentrant tuning, the G and A strings will typically be quite flat (at the 12th fret) when compared to the C and E strings. A compensated saddle makes the bridge a little closer to the nut on those outside strings and a little further from the nut on the inside strings.
You can only do so much with compensation on a saddle blank that is ~ 1/8" wide. I've been able to improve a couple of ukes from being almost 20 cents difference between the outside and inside strings to a little less than ten cents.
You can also adjust this intonation by changing strings - this is why some ukes "like" some strings while others may like different strings. People with "golden ears" may find themselves going crazy trying to find strings that will intonate well up the neck. For example, a friend of mine is blind and has perfect pitch - even after I compensated the bridge on my KoAloha he asked why the intonation was so bad! (Since I've compensated the bridge the KoAloha has under 10 cents difference between the inside and outside strings.) This guy won't play acoustic guitar for much the same reason, and he's had even his boutique electric guitars tweaked and retweaked for perfect intonation. (I used to think I'd love to have perfect pitch 'til I met him - some "epic" recordings of classic rock that I love drive him nuts because of the intonation or tuning issues.)
John