Resolution:
Please make sure that the following steps have been taken into consideration

Firstly,

--Your user ID must have CREATE PACKAGE privileges on the database, or your database administrator must create packages for you.
--Your user ID must be the owner of the package.
--The user ID creating the DB2 packages must have BINDADD privileges on the database. Consult with your database administrator to ensure that you have the correct privileges.

Secondly,

--There is no single package "TIBCO". The DataDirect JDBC and ODBC drivers create    several packages. This is the reason why the first connect with either the JDBC or the ODBC driver takes such a long time.
--You can find out which packages exist with the following SQL command:
select * from sysibm.syspackage where owner = '&ltuser>';
To find out which packages belong to the JDBC driver use this SQL command:
select * from sysibm.syspackage where owner = '&ltuser>' and PDSNAME like 'JDBC%';
To find out which packages belong to the JDBC driver use this SQL command:
select * from sysibm.syspackage where owner = '&ltuser>' and PDSNAME like 'ODBC%';
-- Packages created:
These are the packages created for the JDBC driver:

DDJC330A
DDJS330A
DDJR330A
DDJU330A
DDJC330B
DDJS330B
DDJR330B
DDJU330B
DDJC330C
DDJS330C
DDJR330C
DDJU330C

These are the packages created for the ODBC driver:

DDOS510A
DDOS510B
DDOS510C
DDOR510A
DDOR510B
DDOR510C
DDOC510A
DDOC510B
DDOC510C
DDOU510A
DDOU510B
DDOU510C
DDON510A
DDON510B
DDON510C

Thirdly,

The DataDirect documentation seems to be wrong with regards to the required privileges.
There is no such thing like a "DBA" privilege in DB2 for z/OS.
There is a "DBADM" authority (authority can somehow be compared with Oracle roles) but this has nothing to do with packages.
The closest privilege would be the "PACKADM" or the "SYSADM" privilege whereas the SYSADM privilege is something you never will get due to security policies.

The DB2 user needs the following privileges:
- CREATEIN on the user's schema
- BINDADD
- BINDAGENT

These are the absolute minimum privileges to successfully connect using ADB.

See the "DB2 Universal Database for z/OS Version 8 SQL Reference" pages 1016, 1017 and 1023 for more information.