Sundew must be rezzed when the Runner spends his/her first for Sundew's ability to trigger.
Question[]
If I were to rez Sundew on the runner's turn after he has spent a click, do I get my credits on the next click if the runner does not run Sundew's server?
The question, ultimately, boils down to whether "the first time" is determined in a global sense or a specific sense. If a global sense, Sundew realizes that click one has already passed and thus doesn't produce credits. If a specific sense, Sundew sees only the first click since it has existed and produces the next click.