First, note that arrays know their component type at runtime, but instances of generic classes don't know the generic type argument at runtime. A List<T> cannot create an array object at runtime with the runtime type of T[] without further information, since it doesn't know what T is at runtime. The List#toArray() method that takes one array parameter, uses the runtime type of the passed-in array instance to construct an array of the same component type at runtime. But the List#toArray() with no parameters always creates an array with the runtime type Object[]. So elements.toArray() evaluates to an array instance that always has the runtime type of Object[].
Object[] is not a subtype of T[] (when T is not Object), so assigning this array to this.elements, of compile-time type T[], is wrong. However, it doesn't immediately cause any exceptions, since the erasure of T is Object, so the erasure of T[] is Object[], and assigning Object[] to Object[] is fine. It won't cause any issues as long as you make sure to never expose the object contained in this.elements to outside this object as T[]. However, if you expose the object contained in this.elements as type T[] to outside the class (e.g. a method that returns this.elements as type T[], or if you make this.elements a public or protected field), a caller outside the class might expect T to be a specific type, and that can cause a class cast exception.
For example, if you have a method that returns this.elements as type T[]:
public T[] getElements() {
    return this.elements;
}
and then you have a caller that holds ArrayTypeErasure<String> and it calls .getElements() on it, it will expect a String[]. When it tries to assign the result to a String[], it will cause a class cast exception, since the runtime type of the object is Object[]:
ArrayTypeErasure<String> foo = ...
String[] bar = foo.getElements();