Thanks for the extensive feedback! There's two different kinds of enemies. The ranged ones (with a little arrow indicator) will try to keep distance from the player and will mirror your movements to keep a line of fire. The melee enemies will just rush towards you. I used color to differentiate between aware and unaware enemies. I intended there to also be a difference in the shape of the border to display this difference, but apparently this didn't make it into the final project.
I've also been thinking about ways to encourage the time travel mechanic. Maybe directional shields, to force the player to attack from multiple directions...
I added your issues to the bug tracker, will look at them soon-ish.