Atlantis Summon includes a Bonus Ascension Item Chest that is awarded for every 10 summons. You can claim a maximum of 9 chests during each Atlantis Summon event.
The Bonus Ascension Item Chest includes a guaranteed Rare or Epic Ascension Item. Your progress towards the next chest will carry over to the next Atlantis Summon event if you still have chests in stock. Your progress is shown in the Atlantis Summon view (look for a chest icon). Tapping the chest will show you the amount of chests in stock.