The presidential alert is said to be "directed only to consumer cell phones where the subscriber has opted-in to receive test messages". "Beginning at 2:20 p.m. ET, cell towers will broadcast the test for approximately 30 minutes. "
Sure, they probably could turn your phone into a cyber weapon at any time if they want to, but maybe they prefer to test this during an emergency alert test
John McAfee warned about the emergency alert system being a privacy concern, but the EFF disagrees. https://www.eff.org/deeplinks/2018/10/there-are-many-problems-mobile-privacy-presidential-alert-isnt-one-them