No, they don't at all. In normal JJ2, when you enter a secret level not using the Bonus Signpost, the game saves almost all the information about the state of the level, and transports you to the secret level. When you finish the secret level using End Area, a boss, or I think End Area Warp (i.e. not a Bonus or End signpost), you are taken back to the secret level event in the level you came from. JJ2+ breaks this functionality and uses the next level setting in the secret level for all cases.