Being said that the antimatter - matter reaction is faster than that of a fission and fusion, what if the antimatter cloud found at the center of our galaxy could really able to react with matter from the stars around it and cause a chain reaction of annihilation that spreads through the galaxy?
From the article to which you linked:
The cloud shines brightly in gamma rays due to a reaction governed by Einstein’s famous equation $E=mc^2$. Negatively charged subatomic particles known as electrons collide with their antimatter counterparts, positively charged positrons.
So you see, the very reason that we know it's a cloud of antimatter is precisely because it's already annihilating with normal matter that is floating in interstellar space. This won't create a chain reaction because there isn't that much more antimatter in our galaxy. (If there was, it would have annihilated a long time ago.)
And, as others have commented, the products of electron-positron annihilation (gamma rays) cannot go on to trigger further annihilations, so the idea of a chain reaction doesn't apply in this case.
Here are a few more points to add on to Dmitry's excellent answer.
A chain reaction requires amplification, in the sense that one reaction produces products that then initiate an average of $n$ further reactions, where $n>1$. For example, uranium fission produces neutrons, and if the piece of uranium is big enough and sufficiently enriched, those neutrons are capable of initiating further fissions with $n>1$.
The products of electron-positron annihilation are gamma rays, which don't initiate further reactions, i.e., $n=0$.
Empirically, our galaxy has existed for billions of years, and it hasn't undergone any cataclysm yet, nor do we observe any other galaxies in the universe that appear to be undergoing a cataclysm in the interstellar medium of the galactic core. (There are quasars, but their energy source is matter falling into the black hole at the core, not matter-antimatter annihilation in the interstellar medium.)