Content re-indexing after permissions change

Hi

I have a query relating to the process when a group permission is relaxed and the re-indexing of the related content

For example we have a group which was only accessible for registered users, but it was changed to allow anonymous access as well, the permissions were changed at the group level to allow access to group itself and in the appropriate applications so that anonymous users have read access to the content. 

All is good in the core pages 

But the content remained hidden via search for anonymous users until we did a full re-index 

Is this the expected behaviour ?