The lack of violence in both states during the governorship polls has been noted as a yardstick by the military.
Buratai warned and promised stiff punishments for soldiers who are found guilty of showing support for any political party.
Army boss Buratai has charged his soldiers to capture the Shekau in 40 days.
Tinubu said that there are concerns that some people were trying to entice the military out of the barracks.