When you are using one Apache Solr instance to index multiple sites, you will have contents from all sites in the same index.
To ensure that the search results shows only contents from the current site, you can filter the Apache Solr index based on an attribute called 'Site Hash'.
This attribute is passed by the Apache Solr module every time the site is indexed and is stored together with the related pages.
For those who are familiar with GSA (Google Search Appliance), if you are looking for a "collection" behavior, this filter may be the answer.
Note: the site hash is generated based on the base_url by a function called "apachesolr_site_hash()" once and then it's stored in a variable in your database. So if your sites are sharing the base_url or the database, they will share the Site Hash.
In this case, you may need to add another filter (e.g.: Domain ID if using the Domain Access module).