Which sentence structure is more accurate?
- ... that sounds almost like a command.
- ... that almost sounds like a command.
Both are grammatically correct.
I think that in your specific example, most English speakers would have difficulty saying what the difference in meaning might be.
But if you were to change the verb:
He almost barked like a dog.
(Meaning he did not bark)
He barked almost like a dog.
(Meaning he barked, but maybe he sounded like a seal.)
Those have very different meanings.
My best guess to explain this is that "sounds like [...]" is a phrasal verb, while "bark like [...]" is a verb followed by an adverbial phrase. Some would people would say that "bark like" is incorrect. They might object to "like" and "as" being used interchangeably. They would prefer "He almost barked as a dog." or "He barked almost as a dog."
I think there's no difference whatsoever in the two forms.
They mean exactly the same thing, they're used in exactly the same way, and I see no point in attempting to identify subtle differences that aren't really there.
Having said that, I'm intrigued by this NGram showing that whilst sounds almost like has always been the more common form, almost sounds like has gradually been creeping up over the last century. I really can't explain this shift, but it does seem to be a real effect.
If pressed, I would say #1: it (whatever "that" is) definitely "sounds", it doesn't almost "sound". The almost applies to the degree to which that "sounding" is "like a command".
Edit: Per Jason's comment, I'm inclined to withdraw this answer. I had said "if pressed", because it really looked like an extremely fine point in the first place. It looks as if it was a vanishingly fine point. :)