Considering the Serbs hadn't even replied to the Austro-Hungarian ultimatum yet, I'm still a little confused as to why Russia began mobilising its troops at such an early stage.
You got your dates mixed up.
The Russians told the Serbs to accept the Ultimatum. They did, with the only stipulation that the Hague investigate the killing rather than Vienna. Austria responded by shelling Belgrade and declaring war on July 28th. It would only be on July 30th that Russia began her partial mobilization.