these came from an English act of 1733 - AFAIK they did not apply in the IoM where the poor law was different - presentments were to the Ecclesiastical court which could award payment if the two parties could not agree.
in 19th C you could look at the Chancery Court records as I think this is where you would go to enforce payment .
Your period of 1880 onwards is however after the removal of most social welfare (eg probate) issues from the ecclesiatical courts - however I'm not sure what happened to maintenance of illegitimate children after this