Using a global huge tnsnames.ora file (more than 600k) the start of SQL Tuning module from PAO 126.96.36.199 takes almost half an hour. Using a truncated tnsnames.ora, it takes less than 1 minute. The tnsnames.ora is located on a network drive. If the tnsnames.ora placed on a local drive then the startup is also fast.
The problem is related to startup of SQL Tuning and not how Performance Analysis launch SQL Tuning.
Use a trimmed down version of tnsnames.ora file on the shared drive.
Put the huge tnsnames.ora on a local drive.
Waiting for fix in a future release of QCO SQL Tuning