This implies to me that there will be some sort of genetic signature attached to the virus by the person acting as a vector.
The people don't attach anything to the virus, but the viral genome does not stay constant, it accumulates small changes. Those changes are only passed on to people from where the change originally occurs, other copies of the virus in different people don't change with it.
Some of these changes could have effects on the properties of the virus (making it spread better or worse, cause more mild or severe illness), and changes that substantially damage the virus's ability to replicate and spread will tend to disappear by natural selection. However, many of the changes don't do much at all, for example they might be synonymous mutations via codon degeneracy, or they may change viral proteins or expression in ways that have modest effects.
If you were to sample a population (say, in Victoria AU) and found everyone infected there had a pretty similar version of the virus, with the same differences relative to other circulating strains, that would be good evidence that they all got the virus from a similar origin: maybe one person spread it to others, who spread it to others, and so on.
If, however, you sample a population and find three different strains: one that looks similar to viruses sequenced in the UK, one that looks similar to viruses sequenced in China, one that looks similar to viruses sequenced in Iran, it is more likely that each of those strains came (directly or indirectly) from a traveler from those places. If the security guard story is true, you'd also expect to find different guards with different strains, and then find strains in their communities that match each of the guards (this is assuming you did a whole lot of sequencing, which may or may not be feasible).
The alternative would be that one person brought in a strain of the virus that then happened to randomly mutate to look similar to viruses from all those other places; the chances of that are very very slim.
This is basically the same principle as paternity testing; though using a different type of genetic tool, it relies on genomes in the same lineage being more similar than one would expect by chance.
There is a tool helpful for tracking/visualizing some of these changes throughout the pandemic: https://nextstrain.org/ncov/global