This issue seems to be related to http://jira.atlassian.com/browse/CONF-14137, but i think that it isn't the same.

The livesearch macro ignores the given spaceKey and searches over all spaces. The dropdown results are limited to the given space, but the results on the search result site are not. I've tried spaces with

• all lowercase spaceKeys
• all uppercase spaceKeys
• mixed spaceKeys

but the results always include matches from all spaces.