Works perfectly for me -
SQL> WITH dummy_table AS(
  2  SELECT '3862,3654,3828' dummy FROM dual
  3  )
  4  SELECT trim(regexp_substr(dummy,'[^,]+',1,Level)) AS dummycol
  5  FROM dummy_table
  6    CONNECT BY level <= LENGTH(REGEXP_REPLACE(dummy,'[^,]+'))+1
  7  /
DUMMYCOL
--------------
3862
3654
3828
SQL>
There are many other ways of achieving it. Read Split single comma delimited string into rows.
Update Regarding the duplicates when the column is used instead of a single string value. Saw the use of DBMS_RANDOM in the PRIOR clause to get rid of the cyclic loop here
Try the following,
SQL> WITH dummy_table AS
  2    ( SELECT 1 rn, '3862,3654,3828' dummy FROM dual
  3    UNION ALL
  4    SELECT 2, '1234,5678' dummy FROM dual
  5    )
  6  SELECT trim(regexp_substr(dummy,'[^,]+',1,Level)) AS dummycol
  7  FROM dummy_table
  8    CONNECT BY LEVEL          <= LENGTH(REGEXP_REPLACE(dummy,'[^,]+'))+1
  9  AND prior rn                 = rn
 10  AND PRIOR DBMS_RANDOM.VALUE IS NOT NULL
 11  /
DUMMYCOL
--------------
3862
3654
3828
1234
5678
SQL>
Update 2
Another way,
SQL> WITH dummy_table AS
  2    ( SELECT 1 rn, '3862,3654,3828' dummy FROM dual
  3    UNION ALL
  4    SELECT 2, '1234,5678,xyz' dummy FROM dual
  5    )
  6  SELECT trim(regexp_substr(t.dummy, '[^,]+', 1, levels.column_value)) AS dummycol
  7  FROM dummy_table t,
  8    TABLE(CAST(MULTISET
  9    (SELECT LEVEL
 10    FROM dual
 11      CONNECT BY LEVEL <= LENGTH (regexp_replace(t.dummy, '[^,]+')) + 1
 12    ) AS sys.OdciNumberList)) LEVELS
 13    /
DUMMYCOL
--------------
3862
3654
3828
1234
5678
xyz
6 rows selected.
SQL>