if an intelligence agency figured they could compromise the battery of these devices, they'd have to find a guaranteed way that the enemy were in possession of them. i don't believe that these were just "mass sold to the public" in hopes that hezballah grabbed a few.
further, if they were savvy enough to spike the batteries, surely they were savvy enough to back door a command into the chipset so that specific paged strings were the trigger… not just "some random signal"
no, the coordinated timing suggests to me that these were either engineered by hezballah intentionally (whether known or not by their mules) and they were hacked (or an inside job) or sabotaged by hezballah's supplier.
the attacker would either need to target specific numbers, or send the command over a common pushing channel.
my money would be on a hacked inside job. the precision and timing is incredible.