No, it's a contraction of "has". It's the present perfect tense.

As a native U.S. speaker who doesn't think much about grammar... ...it SEEMS to me that "She already fluffed that pillow" is ALSO correct. Question: "Has she already fluffed that pillow?" Answer: "Yes, she's already fluffed that pillow." Question: "Did she already fluff that pillow?" Answer: "Yes, she already fluffed that pillow." Question: "Do I need I to fluff that pillow?" Answer: "No, she already fluffed it" works, and "No, she's already fluffed it" also works.

It's an abbreviation for "she has" "She has" can be shortened to "she's" in the same way that "it has" or "it is" becomes "it's"