It turns out the words need to be enclosed in parentheses. If I issue
q=fulltext:(marina zadar)
both words are used in the scoring of the documents and the results are ordered as expected. Issuing q=fulltext:marina zadar
looks for the word "marina" in the 'fulltext' field as specified and for the word "zadar" in the field which is set as default for the used query handler in solrconfig.xml.
This might have been a rookie error but perhaps it will help someone in the future.