Okay, here is an example on how Booming Blade -can- be forced.
You've Boomed him, and a Sword and Board fighter marks him. You've Aegis'd some other dude, so it don't matter. But you've been taking the beats so he decides to attack you rather than the fighter, just because you're more likely to go down. He attacks you, so the Fighter steps in and says 'NOT THIS DAY VILLAIN' and hits him using Shield Push feat. The enemy is forced to move one square, and that triggers the Boom of your Boom.
The enemy has moved, it's during his turn, after the beginning, so yeah, Boom triggers.