How to add same preset to all layers?

Save an animation preset using the animated properties, with the CTI (current time indicator) set to the first keyframe. Move the CTI to where you want the next layer to start animating, and then apply the preset you just saved.

A more efficient option would be to use an expression to control the animations using time-InPoint for an interpolation expression like this to move a shape or text layer in from the left during the first 20 frames of the layer.

t = time - inPoint;
w = sourceRectAtTime();
tMax = framesToTime(20);//the move timing in frames;
value1 = [-w.left - w.width, value[1]];
value2 = [thisComp.width/2, value[1]];
easeIn(t, 0, tMax, value1, value2);

 The expression works as long as the anchor point of the text or shape layer is at the default 0, 0,.

You modify it slightly for shape layers or footage, and you can correct it for layer scale and even rotation. 

As long as you use keyframes, the animation will start at the current comp time. You need expressions to force the animation to start based on the in or outpoint of a layer.