Chicken tikka masala isn't completely a traditional Indian dish. The original recipe was created in England, not India, when Brits returning from assignments in colonial India brought back a taste for Indian food (like spiced, grilled meat) and it got combined with English food traditions. Some of the histories I have seen describe "gravies" as being particularly popular at the time chicken tikka masala was created, hence the sauce part of this dish. The rest is culinary history.