Halsey didn't fall for the decoy. He knew that Ozawa's force was a decoy because we were still intercepting and decoding Japanese transmissions. The fact is that Halsey just plain screwed up. He thought Kincaid had the San Barnardino Strait covered and just up and took off after Ozawa with his 3rd fleet.
I guess "fall for" may be too strong. However, his strong desire to race off and bag Japanese carriers and failure to make sure San Bernadino was covered by somebody essentially allowed Ozawa's decoy force to be just as effective as if he hadn't known what its mission was. The Japanese plan was working by dumb luck and only Kurita's timidness off Samar in the face of American courage averted a worse disaster for the US.