Australian scientists develop genome sequencing to trace COVID-19 cases within four hours

Nice development! it will be interesting to see how it is used and if it makes tracing actually easier, my understanding is that RNA viruses are not so easy to sequence and follow between people.

The virus can alter the genetic signature of the hosts as it replicates itself inside them.

This sentence is wrong, the virus can alter its own genetic signature as it replicate inside the host. The virus has no mechanism to alter the genes on human cells.

This is the principle that allows tracing. When patient A is infected a few extra mutations will happen in the virus that were not there before, if later you find patients B, C and D are also infected and only B has a virus with those mutations, it can be said that B got the infection from A, and that C and D got it from someone else.