The most important line from the article
"Alito, handling his first case, sided with inmate Michael Taylor, who had won a stay from an appeals court earlier in the evening."
I think voting to uphold the appeals court's stay on his first day on the job is being cautious not liberal. He needs to get his clerks and himself up to speed. Additionally, he is invoking stare decis which in this case the court has within the last week blocked executions on similar grounds pending disposition.
Hopefully, the delay in these cases will allow the conservatives to speed up future executions and put the smack down on these challenges.
I hope that's the case. I do agree that it's too early to make an evaluation.
(Although I must admit it gave me pause to see him against Roberts, Scalia and Thomas right out of the box.)