Append hint with autotrace
Answer to the original output:
This is not caused by autotrace. You will get the same error even without autotrace, just by repeating the same direct path insert. Issue a commit after the first insert.
This is a documented restriction: ORA-12700 to ORA-19400

ORA-12838: cannot read/modify an object after modifying it in parallel
Cause: Within the same transaction, an attempt was made to add read or
modification statements on a table after it had been modified in
parallel or with direct load. This is not permitted.
Action: Rewrite
the transaction, or break it up into two transactions: one containing
the initial modification and the second containing the parallel
modification operation.

Answer to the new output, after edit:
Ok, so you have a rollback, and you started a new transaction. In this case, autotrace really is the culprit, indirectly. The above rule still applies, and as the above description says, even a read reference will cause the above error. If autotrace is enabled, it implicitly runs something like this (after your original statement was finished):
EXPLAIN PLAN SET STATEMENT_ID='PLUSxxxxxx' FOR insert /*+ append */ into emp_big select * from emp_big_temp;
You can easily confirm this by enabling the errorstack trace for the error 12838 (it is fine in a sandbox environment for this short demo, but this is not how I would do this on a real database):
alter system set events '12838 trace name errorstack level 3';
If I run this now:
SQL&gt; create table t1 as select * from dba_objects where 1=2;

Table created.

SQL&gt; alter system set events '12838 trace name errorstack level 3';

System altered.

SQL&gt; set autotrace on
SQL&gt; insert /*+ append */ into t1 select * from dba_objects;

20079 rows created.


Execution Plan
----------------------------------------------------------
ERROR:
ORA-12838: cannot read/modify an object after modifying it in parallel

I will find the error and a trace file in the alert log. The trace file contains this:
dbkedDefDump(): Starting a non-incident diagnostic dump (flags=0x0, level=3, mask=0x0)
----- Error Stack Dump -----
ORA-12838: cannot read/modify an object after modifying it in parallel
----- Current SQL Statement for this session (sql_id=5x12x8czsd3t9) -----
EXPLAIN PLAN SET STATEMENT_ID='PLUS730007' FOR insert /*+ append */ into t1 select * from dba_objects

And that is what causes the error, because it is still the same transaction. You can test it even without autotrace:
SQL&gt; rollback;

Rollback complete.

SQL&gt; set autotrace off
SQL&gt; insert /*+ append */ into t1 select * from dba_objects;

20079 rows created.

SQL&gt; explain plan for insert /*+ append */ into t1 select * from dba_objects;
explain plan for insert /*+ append */ into t1 select * from dba_objects
*
ERROR at line 1:
ORA-12838: cannot read/modify an object after modifying it in parallel


SQL&gt; select count(*) from t1;
select count(*) from t1
                     *
ERROR at line 1:
ORA-12838: cannot read/modify an object after modifying it in parallel