Hi Oliphaunt182, maybe the next two tips can help you to solve your problem....8-}
First h:commandLink show the values, because the whole page will be build new and therefore the inserted values are part of the page.
Second:a4j:commandLink doesn't build the page, it depends on you which part of the page should be rebuild (=rendered). Have a short look at the associated live-demo component
How to solve your problem fast:
1. add ids to your h:outputText
2. modify the attribute rendered to this ids
Normally this should do the work you wanted to do....
you defined ajaxSingle on the link, so nothing except the link will be processed.