Oracle Database Discussions

I have one user in the database say'user1'. Let this user has only 'create session' privilge.

I have two sessions open. In one session I am connect as:

"sys/oracle as sysdba" and in other session, I am connect as : "user1/user1".

Now from "sys" session I am granting dba privilege to 'user1'. "grant dba to user1".

When I go to "user1" session and fire a command with out reconnecting :
'select * from session_privs', I see the only two privileges

1 . Create session
2. Unlimited Tablespace.

Here I understand that :

1. I need to connect again as user1/user in order to reflect the dba privilges.

2. But even if I do no connect again, why am I getting "Unlimited Tablespace " privilge.

My question is : Is there something special about this privilege or is this a bug?