A third WINZ worker, 43-year-old Lindy Louise Curtis, was also shot and badly injured in the incident.
Tully is facing an attempted murder charge in relation to Curtis' injuries.
Mr Robinson and Mr Jack stated in the review report that the MSD's approach to safety and security needed to be more cohesively planned and formalised.
Recommendations included investigating whether some of MSD's services which tended "to create tension or volatile situations" could be effectively provided in non face-to-face ways.
A review into how security guards were deployed at MSD's sites, what skills were required by security guards and activities that security guards should carry out was also recommended.
The report also found the Ashburton shooting was an "extreme event" and not preventable.
Even if all the recommendations detailed were implemented, "extreme events could still occur", Mr Robinson and Mr Jack stated.