Mysql Explain Query with type "ALL" when an index is used

I ran a query in Mysql like below:

EXPLAIN
SELECT *
FROM(
        SELECT *  # Select Number 2
        FROM post
        WHERE   parentid = 13
        ORDER BY time, id
        LIMIT 1, 10
    ) post13_childs
JOIN post post13_childs_childs
ON post13_childs_childs.parentid = post13_childs.id

and the result was:

id |select_type  |table               |type |possible_keys  |key      |key_len  |ref              |rows    |Extra
1  |PRIMARY      |<derived2>          |ALL  | NULL          | NULL    |NULL     |NULL             |10      |
1  |PRIMARY      |post13_childs_childs|ref  |parentid       |parentid |9        |post13_childs.id |10      |Using where
2  |DERIVED      |post                |ALL  |parentid       |parentid |9        |                 |153153  |Using where; Using filesort

This means it used the index parentid but scaned all rows due to ALL and 153153. Why could not the index help to not Full Scannig?

Although if i run the derived query (Select #2) alone like below:

Explain
SELECT * FROM post  
WHERE parentid=13
ORDER BY time , id
LIMIT 1,10

the result would be desired:

id |select_type  |table  |type |possible_keys  |key      |key_len  |ref  |rows    |Extra
1  |SIMPLE       |post   |ref  |parentid       |parentid |9        |const|41      |Using where; Using filesort

Edit:

The table post has these indexes:

1. id (PRIMARY)
2. parentid
3. time, id (timeid)

count of total rows --> 141280.
count of children of 13 (parentid=13) --> 41
count of children of 11523 --> 10119

When i add index of (parent,time,id), problem of first query would be solved by the explin output for 13 --> 40 rows, type:ref
and for 11523 --> 19538 rows, type:ref!!! this Means all children rows of 11423 is examined while i limited first 10 rows.