The text of the proposal disagrees with your claim. Or - are there lots of Europeans seeking asylum in Switzerland?
Funny enough, the voting of this weekend mentions as argument also "the lax asylum politics in the EU" while exactly THIS weekend the EU is strengthening a lot, and I mean quite a lot, the asylum procedures and including border controls. I guess they had to push it quickly before the Swiss voter notices...
Maybe its a bit like Brexit, i.e. not rational immigration being one of the major issues when it did nothing to reduce the immigration of (non-white) people from third countries and EU migration was rapidly decreasing anyway.