It should be able to accept input before the beat (except for the first one) - but I do like the suggestion to "delay" the actual movement to music.
One save way to attack the first enemy is to jump in after he switched to "Waiting...". His phase will change to "Attack!" which will change to "!ATTACK!" after you hit him - giving you another cycle to safely jump out. But that's just horrible design on my end (oh and sometimes the input doesn't register right, meaning the enemy will attack you nonetheless -_-)
Sadly I cannot reproduce the crash after the time runs out :(
Thanks for your feedback!