Seems to work fine in 1.13c for me, level 20 Evade at 56% chance.
Tested against Zombies and Fallen in normal Blood Moor with a level 99 character, I was running so that hit chance would be a non-factor (autohit). Around half the time I wasn’t getting hit even though I was clearly within melee range and running, it seems that Evade occurs without a sound and without animation.
I’m gonna increase the Evade chance to 100% in skills.txt and see if that changes anything, then I’ll test it in D2R as well. Assuming there’s no hardcoded limit or anything like that. 
Okay, finished the 1.13c test. I set Evade chance to 100% in skills.txt by changing Param1 (min % evade) and Param2 (max % evade) both to 100%, then I ran around in normal Flayer Jungle and was attacked by both melee, ranged, and shaman fetishes.
None of them could hit me with their melee attacks, ranged attacks, or spells (Inferno) while I was running, I only got hit when I stopped moving. Something interesting is that the Evade sound does plays but only for ranged attacks, not melee. I didn’t test to see if spells also triggered the sound but it probably does.
Tested in D2R by doing the same changes to Evade in skills.txt (setting Param1 and Param2 to 100%) and the results are the same.
I went to normal Flayer Jungle again and was attacked by melee, ranged, and shaman flayers and their melee, ranged, and Inferno attacks could not hit me while I was moving. The moment I stopped moving then I was getting hit.
I also went to normal River of Flame to test. Urdars couldn’t hit me with their melee/smite attack, grotesques and grotesque wyrms couldn’t hit me with their melee attack, blood maggots couldn’t hit me with their poison spit, and abyss knights couldn’t hit me with their spells or melee attacks. I was only hit when I stopped moving.
Also yes, spells do trigger the evade sound.
TL;DR: Evade works fine vs melee attacks, ranged attacks, and spells from my testing.