If there was nothing unprotected in your Palace that was attacked by the Cannon, this is indeed not a chase, and thus a draw. In Asia rules a mate threat (even mate in one) is not considered a chase in itself; you really must threaten to capture something on the subsequent move for that. A frequently occurring case is a King behind a pinned Advisor (e.g. by a Rook or together with Elephant by a Cannon), threatened to be mated on the last rank by a Rook. To prevent the mate the King steps aside, but then a check with that same Rook from the front drives it back behind its Advisor, after which the Rook resumes its original location to threaten the back-rank mate. This counts as 1-check, 1-idle, and thus a draw. Even if the mating square contained an unprotected piece (say the other Elephant), the 1-check + 1-chase is also allowed (under the general rule that alternately chasing different pieces is allowed).
If there was nothing unprotected in your Palace that was attacked by the Cannon, this is indeed not a chase, and thus a draw. In Asia rules a mate threat (even mate in one) is not considered a chase in itself; you really must threaten to capture something on the subsequent move for that. A frequently occurring case is a King behind a pinned Advisor (e.g. by a Rook or together with Elephant by a Cannon), threatened to be mated on the last rank by a Rook. To prevent the mate the King steps aside, but then a check with that same Rook from the front drives it back behind its Advisor, after which the Rook resumes its original location to threaten the back-rank mate. This counts as 1-check, 1-idle, and thus a draw. Even if the mating square contained an unprotected piece (say the other Elephant), the 1-check + 1-chase is also allowed (under the general rule that alternately chasing different pieces is allowed).