Just got new Kumho Ecsta ASX and I notice even tho the outside labels are facing outside but the tire tread pattern are opposite of eachother. Is it suppose to be like that?

 

There should be arrows on the side wall that point the direction of rotation. You don't say whether each side is different or front to back. Either way the pattern needs to be going all in one direction.

Some people really don't know what they are doing when it comes to uni-directional tires.

I bought a used XK8 and the rear tires were backwards.

 

Yes - the ASX has specifically formulated tire compounding such that the 'grippier' rubber is intended to be mounted outboard, while the rubber more suited to wet weather driving is mounted inboard on all four corners.