An implosion is a region of low pressure collapsing because of the higher pressure surrounding it. That's clearly not what is happening when a balloon 'pops', as the sound that is produced is the high pressure air rushing into a lower pressure environment. Much like traditional explosives, when a balloon pops you have an area of concentrated matter expanding into the area of lower concentration.
Also, it is functionally the same thing as a car tire popping which clearly looks like an explosion: https://youtu.be/HANwJp8Z5mc?t=27
Comments in another answer made me realize the obvious connection between balloons, rockets, and bombs. If you fill up a balloon and let the air out the balloon will fly around the room like a rocket. Rockets don't explode because like the balloon they have a big hole to give the explosive material a way out.
If you instead fill up a balloon and prick it with a pin, the hole the air escapes from is much smaller. Much like people trying to quickly escape a building, this creates a crushing force at the exit, air molecules in a balloon do the same thing. Those air molecules have so much force that they can expand the hole in a destructive way which pops the balloon. This is what happens to rocket when the explosive material can't escape fast enough, it becomes a bomb!
So a balloon is essentially either a rocket or bomb depending on how exactly the air is escaping from it.