Given a graded manifold with symplectic form $\omega$ of degree $n$, I have seen two expressions for the corresponding Poisson bracket of degree $-n$. Cattaneo-Fiorenza-Longoni, http://www.math.uzh.ch/fileadmin/math/preprints/15-05.pdf in section 2.7, give $$\lbrace f,g \rbrace=\iota_{X_{f}}\iota_{X_{g}} \omega,$$ while Cattaneo-Schatz, arXiv:1011.3401 in example 4.9, give $$\lbrace f,g \rbrace=(-1)^{|f|+1}X_{f}(g).$$

It seems to me that it is the latter that gives the proper graded anticommutativity so that the Poisson bracket is a Lie bracket of degree $-n$.

Is one of the two definitions mistaken or is it a matter of differing conventions?