This was covered by the Skeptics' Guide to the Universe, episode 317.
Electric, digital clocks keep time by using the frequency of the power lines to keep time (60 Hz in the US, and 50 Hz in Europe).
If you change the frequency of the AC current, you will change the pace of the clock.
The frequency of the AC current coming out of power plants does regularly fluctuate, but that fluctuation is regulated such that the correct number of cycles happens in each day. (Wikipedia:Utility frequency stability)
In North America, adjustment occurs whenever the error exceeds 10 seconds (in the East), 3 seconds (in Texas), or 2 seconds (in the West). (See Manual Time Error Correction)
The synchronous grid of continental Europe is re-calibrated every morning at 8:00am. You can see the real-time frequency at http://www.mainsfrequency.com/.
Italy is part of this synchronous grid, but Sicily being an island, this connection is via a single underwater cable.
During the time of this Volcanic eruption, for about 20 days in May, this cable was disconnected for routine maintenance. Sicily relied largely on its local hydro power. The more unstable hydro power production combined with the smaller Sicily-only grid resulted in the clock error.
This article and this article (both in Italian) tell the story.
The power supplied to users has fluctuated between 50 and 50.13 Hz, creating small accelerations in timer appliances.
It will happen again at the next detachment from the continental network.
Not only common alarm clocks, but also microwave ovens and appliances with timers are victims of hectic times.
The Daily Mail claimed that watches were also affected, but that is impossible. Skeptics Guide speculates that either it was mass delusion or poor reporting or mistranslation on the part of the Daily Mail.