Russia didn't mobilize until July 31st. You haven't really grasped the timeline, have you?!
As for Serbia mobilizing, that was Austria's intention when it placed the 48 hour time limit on its ultimatum. Of course Serbia mobilized after recieving such harsh demands, as they could only be viewed as an Austrian excuse for war due to their undiplomatic nature. Well, Austria got what it wanted. Serbia did indeed mobilize.
But Austria got two things for which it *didn't* want or expect, as well. The first was that Serbia caved to 3 of Austria's 4 main demands, and suggested that the 4th Austrian demand be submitted to the Hague for arbitration. This acceptance of Austria's harsh terms (no term was outright rejected per Austria's plan) was unexpected.
Austria's second surprise was that after it invaded tiny Serbia, that the Serb Army roundly beat the Austrian invasion force. It took another full year, and the combined might of Germany, Austria-Hungary, and Bulgaria to finally conquer Serbia.