The negotiations between England and Russia were no secret; Franz in distant Vienna received the news, and even the content of the discussions had been largely restored.
Everyone understands the principle of holding out for a better price. The Russians intentionally leaked the information, clearly waiting for Austria to make an offer.
It doesn't have to be higher than the British offer, just close enough, and the Tsarist Government would definitely choose to stand with Austria.
It's determined by interests; the value of the Russian-Austrian Alliance is much greater than that of a British-Russian alliance, and besides, the British are not going to form an alliance with them.
Open a map and you'll see, the long border between Russia and Austria, there's simply not enough natural barriers to serve as a line of defense. Without the alliance, just the pressure of national defense alone would be a headache.
