Commands have delayed execution

The bug

This bug is hard to put into words. Commands that change position, or refer to an entity's position, are consistently "falling behind," or are delayed in some fashion.

To reproduce

Place down a repeating command block with this command inside, and power it:

/execute @p ~ ~ ~ execute @s[r=0.01] ~ ~ ~ say "Hello, me!"

It's running a /say command as the closest player if they can be found within one-hundredth of a block of their own position.

What I expected:

For the /say command to fire every time this command is run in every circumstance, whether the player is moving or not.

What happens:

The command fails if the player is moving (walking, jumping, and falling, for example) because it cannot find the player within one-hundredth of a block of themselves. This also applies to non-player entities.

This affects more than just a simple distance selector argument. This delay can be felt through relative and local positioning, and through function files.