Let's clarify some terms first. My understanding of "Links Popularity" is, it's about the number of links pointing at your site, incoming links. The logic is, more links pointing to a site implies the site is more popular, hence higher quality. Based essentially on quantity.
As to outgoing links (and incoming links) there is another aspect, not sure of the buzzword, that relates to themes and link relavancy. Hence the mixed reviews of links popularity programs. Links pop works well on Google for example, relavent links works better with AV. The links are evaluated for quantity AND relavance (quality).
If you open your new window using the target="_blank" option in a standard href tag, the spiders will follow the link just fine. If you use a script, some nonHTML method, it will depend on the method.