Come to think of it, with my Santa Fe XL, I though my tilt feature was broken for the longest. Then out of the blue, it would work, then stop working....back and forth like this, but very random, no rhyme or reason, sunny or raining, cold or hot, etc. I did some research and discovered that it will only tilt down if the selector switch (for adjusting the right/left mirrors) is in either the right or left position. If the selector switch is in the neutral position, the middle, they will not tilt.
So, at this point, I do not know if they do or don't tilt on the Ultimate (Canadian). I am guessing they do as Pipewrench said his Limited does. I have not taken delivery yet, just found out it may be this Sat fingers crossed. (White with black nappa)