Thank you for your input! 
I double checked, and Endnote is updated. Updating citations and bibliography does not make a difference. However, I realized a new thing, that might be of importance.
At the moment my document looks like this:
“…in several national and international political documents.11-14 The WHO {World Health Organization, 2002 #65} has explicitly encouraged…”
Here you can see the inserted citations from some days ago, using JAMA style, followed by the citation style as it appears since yesterday.
When I convert a copy of this text to unformatted citations, everything is aligned as such:
“… in several national and international political documents.{World Health Organization, 2008 #26;Helse- og omsorgsdepartementet, 2013 #29;Ministry of Health Services 2014 #93;World Health Organization, 2002 #65} The WHO{World Health Organization, 2002 #65} has…”
Interestingly, when I then want to convert it back to formatted citations, the text appears not as shown in the upper example, but as in the last example.
Does that maybe give any clues as to what the problem could be?