We don't normally add Note that for normative text, or comments like "random behavior". Using dashes like that isn't good practice for formal english.

The startup phase is not part of the application execution, so this update is also incorrect. AIUI we are trying to say "Any operation of <tt>BeanManager</tt> may be called at any time during the execution of the application. Some <tt>BeanManager</tt> operations may be called during application initialization."