Same source, I used the graph generator to graph by country and year. The bottom 'light green' bar in each country's section is 2015, each successive bar above is one year prior.
You can see, in 2015, very notable increases in (in)migration rate for Austria, Denmark, Germany, Ireland, Malta, Slovakia, and Estonia. You can also see Italy's huge 2013 spike (in magenta).
I'm looking at the top graph (EU 28 countries) and not seeing anything alarming relative to prior years. I'm not sure why Europe should be disintegrating now and not a decade ago if the claim is solely that Europe's problems are due to migration.
http://imgur.com/a/od7Hi
You can see, in 2015, very notable increases in (in)migration rate for Austria, Denmark, Germany, Ireland, Malta, Slovakia, and Estonia. You can also see Italy's huge 2013 spike (in magenta).