Are deleted posts still reflected when viewing a member in the Administration console?

Your picture is specifically looking at questions in a forum for that user.  The posts count would include posts in other applications (Ideas, blog posts, forum discussion posts, etc).  If you have reporting available, viewing the content report filtered to the user in question will give you a better idea of all the user's posts.

Should also mention, that fields has been pretty inaccurate in the past since it just gets incremented when a post is created (or decremented when one is deleted).  There was no process to ever correct it if it got out of sync.  That was addressed in Version 12. After the fix the field is always completely recalculated whenever there is a change, so if it was ever out of sync, any future new or deleted post would cause the recalculation and correction of the value.  The Posts field in member admin also links directly to the Content Report (if avaialable) in version 12.

Your picture is specifically looking at questions in a forum for that user.  The posts count would include posts in other applications (Ideas, blog posts, forum discussion posts, etc).  If you have reporting available, viewing the content report filtered to the user in question will give you a better idea of all the user's posts.

Should also mention, that fields has been pretty inaccurate in the past since it just gets incremented when a post is created (or decremented when one is deleted).  There was no process to ever correct it if it got out of sync.  That was addressed in Version 12. After the fix the field is always completely recalculated whenever there is a change, so if it was ever out of sync, any future new or deleted post would cause the recalculation and correction of the value.  The Posts field in member admin also links directly to the Content Report (if avaialable) in version 12.