I actually found the problem. The data sheet said that the interrupt bit (0x2F) needed to be set to 1 to be set to INT2, when it really needs to be set to 0 to go through the second interrupt pin. I just needed to change what I was writing to the interrupt map register (0x2F) from 0x10 to 0x00.
If anyone is using the ADXL345 accelerometer and is having similar problems, another issue I found is that you can’t have the accelerometer running the autosleep function if you intend to use it to wake up the Particle from sleep. It will never wake up on move in that case.