GMMichael
Guide of Modos
The ability only lasts for your current turn, and includes all of your movement even if you attack mid way through, open a door, fall prone and stand up afterwards.
Your turn. Your movement. Simple.
Funny, I didn't read any of that in the OP's rule quote. It doesn't say "you get a bonus to AC for your turn." It says, "when you move . . . until you stop moving."
Now, let's look at some official WotC guidance, since I'm not (yet) trying to read into it. The online Player's Basic Rules says:
First, this is called "Breaking Up Your Move," not "Continuously Moving." Second, when you move another 20 feet, it doesn't say "keep moving your next 20 feet." Or, "continue moving the rest of your movement." If WotC wanted to imply uninterrupted movement, they failed miserably.You can break up your movement on your turn, using some of your speed before and after your action. For example, if you have a speed of 30 feet, you can move 10 feet, take your action, and then move 20 feet.
NOW to read into it, look at the Rules As Intended. The feature is called "Evasive Footwork." If you're attacking, you're probably not evading. If you're taking any other action, (besides Disengage or Dodge) you're not focusing on being "evasive." Why would they give it that name, if you could attack, cast a spell, search, use an object, or do whatever, while doing it?
For those of you who actually care about RAI, you see what I mean. For you RAW folks . . . hold your breath for an official clarification. Keep holding. A little longer...