Please check your units for the relief setting. I believe that you refer to 0.065 bar and -0.004 bar (ie 6.5 kPa and -0.4 kPa), although you may wish to check the pressure / vacuum limits with API 650 Clause 3.2.1.and the tank nameplate for design pressure, just in case you missed something.
The hand pump might give you 6.5 kPa air pressure, but no vacuum, provided you have an accurate gauge for measuring that pressure. Most impostant, if your tank is rather large in size, it will take you weeks to generate the 6.5 kPa with a hand pump, for testing the relief valve. Also, you might wish to review the testing method of the relief valve installed on the top of the tank.
Best of luck,
gr2vessels