The authenticated encryption mode devised by the Keccak team is the SpongeWrap method, and is first described in this paper — the paper you cite is an amalgamation of all their major sponge papers. The encryption method wrap is described in Algorithm 3, on page 10. In particular, lines 14–18 absorb-squeeze with respect to the ciphertext.
In practice it is probably simpler to think of it in the following way:
To implement this in terms of absorbing and squeezing, we have to use the squeezed output from the previous iteration (here called $s_r$, called $z$ in their algorithm) and xor this with the message, before absorbing in the message as part of the next call. In my mind absorbing / squeezing is a much less clear way of describing the process, but mathematically it is important since it clearly shows the object to be an instance of a Duplex Object, which is itself a series of sponges, and thus allows us to use their security proofs.
I do not know of any test vectors for SpongeWrap.