Competitor Products ASINs
Within Automatic PPC campaigns Amazon will also display your (Sponsored) products on the listing pages of other similar products:
Example of Sponsored Products on Competitor Listings
These kinds of ads can only be generated via Automatic campaigns (and sometimes via broad/phrase Manual Campaigns). It is not possible to actively place ads in manual campaigns for ASINs.
There are, however, ways to deal with ASINs from search term reports:
How to make use of well running ASINs - Make use of the ASIN's top Keywords
Although you cannot actively place ads directly on the listing pages of these ASINs, there is an attractive alternative. This requires you to research the keywords via which the respective ASINs were found by customers. To do this you can
a) check the keywords in the product's title or
b) check Sonar's Reverse ASIN lookup. Sonar will display the keywords for which the respective ASIN is ranking on the first search result pages.
If these keywords are then placed into the backend keywords or title of the sponsored product, it should appear more often on the respective ASINs' listings. Additionally, when placing ads for the respective keywords from Sonar, you can make potential customers aware of your product even before the competitor ASIN is found.
How to deal with negative ASINs - Avoid Keywords of the ASIN
In general, Amazon should recognize that the respective ASIN is not working for your campaign and will stop displaying the ad on the competitor listing after a few clicks.
You may, however, use the same tactics mentioned above and for example, put certain keywords from Sonar into your negative keyword list.