Retroactive Mitzvah

The Minchas Chinuch (mitzvah 9) questions if the mitzvah of תשבתו שאור מבתיכם is a positive mitzvah that one must remove chametz or it is a mitzvah one fulfilles by simply not owning any chametz.  He brings many proves both ways.
The Alter Rebbe has a third approach.  He holds (siman 431 and explicitly in siman 446:2) that when one doesn't own chametz when it comes the time of the issur, then one retroactively fulfills the mitzvah that s/he did to remove the chametz.
The Rema (434:2) rules that one should be מבטל the chametz only after burning it in order to fulfill the mitzvah with one's own chametz.  What does the Rema mean, we burn the chametz before the time of the issur, so seemingly we can only fulfill the mitzvah by simply not owning chametz, so what difference does it make if you burn the chametz before or after bittul?  However, in light of the Alter Rebbe it is understood for the mitzvah is fulfilled by your actions retroactively when it comes the time of the issur, hence, you want to burn your own chametz (based upon shiur by R' Chayim Sholom Deutsh.)