Not exactly. Saying it needs to be done would look more like “Las sillas deben ser / deberán ser apiladas […]”

Native here.

“Apila” is refering to the listener as “tú” (a.k.a. “you”).

“Apile” is refering to the listener as “usted” (basically a more formal version of “you”).

In Spanish, despite both “tú” and “usted” refering to the 2nd person singular, different conjugations are used in each of them. “Tú” uses the standard 2nd person conjugation, while “Usted” picks the 3rd person’s one instead for whatever reason.