There is only manual claiming in the ZIL staking option. The first reward will appear in 24-48 hours after delegating, next rewards will come to your address about every day — at the end of every epoch. Keep in mind that the network charges fees from your address for every claiming operation. Don't worry, it's not necessary to claim ZIL every day, just don't forget to withdraw it to your wallet from time to time: Open your ZIL wallet and click Staking, then Claim.