The first beta of iOS 8.4 was released back in April. Later in same month, i0n1c was actually the first one to jailbreak iOS 8.4. He demonstrated his jailbreak, likely using different exploits than the ones used by TaiG, on an iPhone 6 running iOS 8.
Taig 2.3.1 Detail
Taig 2.3.1 Download Related Software Screenshot