Parallel Composition of ($\epsilon, \delta$) differential privacy
Your conjecture seems correct. If the sets are disjoint then the mapping $\bar{M} = (M_1,\dots,M_n)$ is $(\max(\epsilon_i),\max(\delta_i))$-DP. Note that for every database $D$ and any $x$, $\bar{M}(D)$ differs from $\bar{M}(D\setminus {x})$ in only one coordinate by the disjoint assumption, w.l.o.g., they differ in the $j$'th coordinate. Therefore, the difference between the density functions of $\bar{M}(D)$ and $\bar{M}(D\setminus {x})$ is the same as the difference between $M_j(D)$ and $M_j(D\setminus {x})$.