Security (CPA?,CCA?) in Authenticated identity-based encryption
The eprint version has the following to say (adapted for your notation):


  Authenticated-decrypt: [...]
  Check that $s = H_3(\gamma, Msg)$. If not, reject the ciphertext, otherwise output then plaintext $Msg$.


In the attackers case, the decryption oracle would try to check if $s = H_3(\gamma', Msg)$ with $\gamma'=\gamma \oplus H_{2}(a,s) \oplus H_{2}(t,s) \oplus H_2(a, s) = \gamma \oplus H_{2}(t,s)$. This leads to a wrong hash and the oracle rejects the decryption before giving any useful information to the attacker.