Ok, i solved it myself.
There where actually two problems:
I use a Apache server to generate previews for PHP files and there was a configure error in my Apache config. The other problem was, that the Apache example config in the FirstSpirit documentation doesn't cover the case, when a project has it's own WebEdit application.
I had to change the following options:
Old rules:
RewriteCond %{REQUEST_URI} !^/fs5preview/preview_cache
RewriteCond %{REQUEST_URI} !^/fs5webedit/preview_cache
New rules:
RewriteCond %{REQUEST_URI} !^/fs5preview/preview_cache
RewriteCond %{REQUEST_URI} !^/fs5webedit/preview_cache
RewriteCond %{REQUEST_URI} !^/fs5webedit_[0-9]*/preview_cache
RewriteCond %{REQUEST_URI} !^/fs5webedit_[0-9]*/preview_cache