How can a decomposition reaction be exothermic?
It just can be so.  Look for something that is favored by cooling instead of heating.
In the case of decomposition of something to pure elements that is exceedingly rare, but decomposition involving other compounds offers more possibilities.  During hot processing of steel (in the hot rolled coil, actually) we can get this reaction which is favored by cooling below 570°C:
Wustite --&gt; Magnetite + Iron
$4 \ce{Fe_{1-x}O} \rightarrow \ce{Fe_3O_4}+(1-4x)\ce{Fe}$
$x$ typically 0.05-0.10.
See the phase diagram here noting what happens to the $\ce{Fe_{1-x}O}$ phase on cooling.