*sigh* This is going to be a fun relationship. I'm a software engineer, not like it matters. And I know how this game is programmed, as it's the same engine specifics as previous games (and if it isn't I'd eat my hat).
Here's some air dodge frame data, I'll base things off of this
invincibility begins on frame 2
invincibility ends on frame 23
can act again on frame 30
Your IASA (or FAF) or whatever, is frame 30, meaning you can take any action on frame 31. Including another air dodge, a special move, an aerial, a jump. Anything (that's valid in the air).
Meanwhile, a separate flag that exists for all aerial actions is known as the auto-cancel flag. This is a flag for any animation that states that you will stop (or start) incurring this animation's designated landing lag from this frame onwards, otherwise you will be dealt with a normal landing (this is 4 frames).
Usually, this is the same frame of the IASA at the latest, or otherwise earlier.
In this game, the auto-cancel flag starts frame 1 of the air dodge, and lasts until (rough guesses, but seeing as I can short hop air dodge and land as Marth without lag) frame 40. Meaning that if you land any time in the 10 frames after you can act you will incur the air dodge landing lag (22 frames).
Every time you start another animation in the air, the auto-cancel flag will be reset. This has been like this in at least Brawl and this is the case here. A lot of aerials in this game have the auto cancel flag enabled the moment you start the animation of an aerial, the other common case is that it is enabled only the frame of the attack coming out, meaning that characters with these specifically programmed moves are "chosen" by Sakurai. Otherwise, characters can opt to start another move that has less landing lag than the air dodge and can deal with that instead.
Nothing I've said is accidental. When we start getting the dumped data files of character air dodges it will literally have a script as such:
1: Auto Cancel Flag Disabled
2: Invincibility Flag Enabled
23: Invincibility Flag Disabled
30: IASA
40: Auto Cancel Flag Enabled
and there was specific instances in Brawl that characters had this post-animation auto cancel flags (Meta Knight's up air, Donkey Kong's back air). There's no indication that something as paramount and likely individually programmed into 51's characters air dodge animation data was an exploit or not done by design.
What's the logic for this choice? Seems obvious... get rid of mindlessly air dodging into the ground, why does the auto cancel frame happen after the move ends? I really could only guess;
personally I wouldn't mind it getting patched so the IASA matched the auto cancel (i.e. 40 frame air dodge). Considering that the auto cancel flag was NEVER disabled for air dodges in Brawl, it's a HUGE mechanic change.
How is it some unintended bug that players can act when the game tells them they can act?
Either way or otherwise, try to be more careful about your ignorance in the future...