The default browser setting is to have all affiliate links opened in the same browser's tab unless this is specifically defined with a code.
Adding (target="_blank") at the end of the URL enables the link to open up in a new window.
<a href="https://shareasale.com/r.cfmb=bannerid&u=affiliateid&m=merchantid&urllink=&afftrack="target="_blank">test</a>
For banners, make sure the (target="_blank") is added at the end of the URL within the href tag.