Those two conditions don't exist. Do you mean "is moving" and "on moved"? Either way, the principle is the same:
The first group of platform conditions are perpetual. Construct will test to see if those conditions are ever taking place and, when they are, will do whatever actions you specify every tick that those conditions are met.
The second group (the animation triggers), is only triggered once for each time the condition is met, indicated by the little green arrow as part of its icon.
Going with the movement I mentioned above, you'd use it as follows:
(1)-Player.platform(on moved) set animation to player.animation "WalkStart"(play from beginning)
(2)-On animation("WalkStart") finished
-Player.platform(is moving) set animation to player.animation "Walking"(play from beginning)
If that still doesn't work you should post your capx so we can take a look through it and point out specifically where you've gone wrong.