When does a paid research assistant become a co-author?
The decision of whether someone should be a coauthor is completely independent of monetary compensation: authorship depends on what sort of intellectual contribution each person has made, and it would be unethical to treat them differently based on their job (paid assistant, student, colleague, amateur, etc.).

People in different roles may be treated differently based on their contributions.  For example, an assistant who does no creative or insightful work, but instead just carries out explicit instructions in a straightforward way, should generally not be a coauthor.  (Still, the assistant should be thanked by name in the acknowledgments.)  When the assistant's work starts to involve exercising nontrivial skill and judgment, coauthorship may be appropriate.  If the assistant is doing a serious part of the creative intellectual work, then coauthorship is mandatory, even if the supervisor's role is deeper.