Yes, it is most likely that the movement is being locked before you have time to move to a safe direction. That window of safety gets smaller and smaller fairly quickly.
I imagine we probably should have had some sort of visual indicator to show the player when they are beyond the locked off point because it can definitely feel like it is a UI response bug.
You have to be pretty quick to get past the second foe (the first foe, I think, is fairly straightforward) and it gets even tougher beyond that.
It's definitely tough though. Probably the toughest game we have ever made. I wrote the code and I still find it pretty challenging. But, yeah, like Poly said, figure out which is the warning phase and which is the attack phase and use that warning phase to avoid being hit and do it fast.
If you are still having problems, let us know here and I can give you a technique hint I use to make it slightly easier.