I got emp points for buying shop items, went to claim them (bc I have that Elite pack for 30d) and I did not get those as well

The "Reward Credits" are delivered to your Item Claim, but the "Reward Points" are added to your Account's Balance, which progresses you up towards the next Tier. There is a little circular icon ( to the right of an Elite Icon ) which displays your Tier Number, and if you click it, will bring up your TERA Rewards Menu and the Rewards Emporium Shop.