I submitted an application for reconsideration without filing a case, and the receptionist said it would take 30 working days to reply. Is it legal for netizens' public security organs to handle this?

This is legal. Where there is any conflict between the two clauses you mentioned, Article 35 of the Procedures for Public Security Organs to Handle Criminal Reconsideration and Review Cases stipulates that these provisions shall come into force as of 20 14 1 1. Where the relevant provisions formulated by the Ministry of Public Security before the promulgation of these Provisions are inconsistent with these Provisions, these Provisions shall prevail.