If you read the actual paper:
http://www.nature.com/articles/ncomms13712
you will see how there is nothing "urgent" or "immediate" or even "soon to be expected", the scientist created a model that seemingly shows that eventually an eruption may happen, but without any clue if it will happen and more than that when it will happen:
"Caution is therefore prudent when forecasting the future mid- to short-term evolution of any period of unrest. Even if the magma underneath CFc is likely to be approaching the CDP, the possible future scenarios can be complicated by additional processes that have not been considered here. For example, increases in the melt liquidus due to H2O release and consequent magma crystallization could increase the melt viscosity, and therefore act against further magma migration. Additional careful scrutiny of monitoring data in the coming months and years is key to interpreting whether hydrothermal heating or magma quenching will prevail."
And as well in one of the two articles you posted:
"This is apparently better news, at least for now; activity in which magma moves upward and accumulates tends to be associated with an increased chance of an eruption. However the change from hydrothermal to magmatic activity can take place at any time, so we're not in a position to say that everything is well under the Campi Flegrei. The Campi Flegrei is still a very volatile place. What it does show is the difficulty in interpreting the data, even from one of the most-studied volcanic areas in the world. Reconciling all of the data is a major issue, despite our efforts."
The Vesuvio and the Campi Flegrei are anyway monitored: http://www.ov.ingv.it/ov/it/vesuvio/statoattualevesuvio.html
The institute publishes weekly and monthly reports:
http://www.ov.ingv.it/ov/it/campi-flegrei/monitoraggio/272-c...
http://www.ov.ingv.it/ov/it/campi-flegrei/attivita-recente/2...
The whole area is "at risk" of course, and it is very likely that something may happen, but whether it will be an earthquake (a major one, as minor ones are daily) or an eruption and when it may happen is something noone can say.
