Have you installed the latest type definition for an asynchronous library?
npm install --save @types/async
I just checked their source and it should accept both an array and a collection:
export function each<T, E>(arr: T[] | IterableIterator<T>, iterator: AsyncIterator<T, E>, callback?: ErrorCallback<E>): void;
export function each<T, E>(arr: Dictionary<T>, iterator: AsyncIterator<T, E>, callback?: ErrorCallback<E>): void;
export const eachSeries: typeof each;
, tsconfig.json "typeRoots": ["node_modules/@types"], .
. , Array<T> T[].