ECAM logic for Ground and Air Engine Fire are different.
On the ground the ECAM includes the lines for shutting down the other Engine BUT after the Fire warning goes out the ECAM removes these lines to shutdown the other Engine.
Hence you can still leave it running unless you do wish to shutdown and get out!!
That is what I was shown in the Sim, sit on your hands for a few seconds after you discharge the bottles, if the warning goes out then the ECAM reconfigures itself.
I've seen this in the Sim. We carried out an RTO due Engine Fire, ran the ECAM and were about to shutdown the other Engine when the Sim instructor said.
"Hold on, give the ECAM time........see now the Fires out the ECAM has removed the shutdown other Engine and EVAC lines"
Don't rush too much, give it a little time. Time you will be using to decide the need to evacuate or not anyway while you discuss with Fire services, ATC cabin crew etc.
Most likely you will shutdown the other Engine anyway after Fire services arrive. But at least you will have time to start the APU to provide power especially at night.
Each situation will be different and you will have to make decisions at the time just be aware the ECAM removes those lines after the Fire goes out...
