The Rune Chests don't actually go to your base, even though that is what the animation currently depicts (we hope to have that fixed in a future release).  Rune Chests live in your Runes screen.  Tap on any Tower, go to, "Edit," and you'll see all of your Rune information.  In the upper right, press, "Get Runes," and that will take you to the Rune Chests.  There's a counter in the upper right to show you how many you have.