HOWEVER, if I were to change this value to something else - ideally this would update the PositionID in the Applicants table for that applicant, but instead it changes the value associated with the PositionID in the Jobs Positions table.
That should not happen. You should check the design of your layout to make sure that you are modifying Applicants::PositionID and not Job Positions::Position ID when you edit the value in this field.
You might also consider the fact that applicants may apply for multiple positions either at the same time as time passes and new positions become available. That gives you the need to link one applicant to many positions as well as one position to many applicants--a many to many relationship that will be best managed by inserting a join table in between Applicants and Job Positions.
Not only can such a table manage the many to many linkage, data specific to one applicant's efforts to get one specific job can be documented in fields defined in that join table. That allows you to record which applicants, for example, get selected to interview for a specific position if you had fields for that purpose to the join table.
Applicants::__pkApplicantID = applicant_position::_fkApplicantID
Job Positions::__pkPositionID = applicant_position::_fkPositionID