That's incorrect.
There are what I would consider valid statistical and criminological reasons for the claim that Australia did not suffer a single gunman spree killing between 1996 and 2019 - and that is the actual claim made, although it's sometimes simplified to 'no mass shootings' , but even if you discount those reasons, this is not the third such incident.
It's the fifth.
Oakhampton Heights, New South Wales, 20th March 2005 - Sally Winters shoots dead her husband and two children before killing herself (three murders, four fatalities (including the perpetrator)).
Hectorville, South Australia, 29th April 2011 - Donato Corbo shot and killed three people and wounded three others in an attack on his neighbours, and subsequent siege by police. (Three murders, three woundings, perpetrator arrested).
Lockhart, New South Wales, 9th September 2014 - Geoff Hunt shot and killed his wife and three children before killing himself (four murders, five fatalities (including the perpetrator))
Osmington, Western Australia, 11th May 2019 - Peter Miles shot and killed his wife, granddaughter, and four great grandchildren, before killing himself (six murders, seven fatalities (including the perpetrator))
I actually do think there are reasons why the Australian statistic is cited the way it is - none of the above were spree killings and that is what the Australian statistic relates to even if some people misrepresent it by simplifying it in their reports - but if you're going to use the measure I think you are using (and I think I'm interpreting you correctly - and it is a valid and truthful position), then you should probably be talking about four previous incidents not two.
Note - I am not including in this the Monash University Shootings, because only two were killed, the Wedderburn Shootings, because only two were shot and killed on that occasion, although a third victim was murdered by stabbing, or the Moorabbin Police Murders, because only two were shot and killed - none of those reach the (admittedly somewhat arbitrary) definition of three shot and killed, that is used to define a mass killing. There could also be other cases where two were shot and killed that I am not aware of.
I am using a metric of four people killed, other than the shooter.
That is why I only come up with three.
Thanks for the overview.
Definitions are important. One way to lie with statistics is to change the definition, or use different definitions for different data sets.