Is our garden on steroids?

I want to preface this by saying the garden is surely NOT on steroids, or anything else for that matter.  I put some compost in, tilled it up this spring, water it sporadically, and generally neglect it.  The dog, since discovering rabbits frequent it despite the fence (they get in below the neighbor's fence) now considers it his personal hunting estate, hiding under the tomatoes and belly crawling toward the carrots.  This is really the extent of care (or neglect) the garden has received.  

Yet, mysterious things have been happening in the bungle-garden.  For one, ground cherries, tomatoes and snapdragons are coming up.  Which wouldn't be weird, since I planted all of these things, but is weird since I planted them LAST YEAR.  What is going on?  Was it the tilling?  These aren't little tomatoes, either.  Some of these plants are attempting to take over the garden.  They're huge.  They are growing from seed (which up in Minnesota isn't supposed to happen unless you start indoors) without cages. There has been at least ten of these garden crashers this year.  I have let a few live if they are respecting the plants I spent money on. Others have met a much sadder fate (me yanking them out with a dumbfounded look on my face).  

Okay, so ghosts from summer past is the first weird thing.  The second also involves tomatoes, these planted by me this year.  Heirloom tomatoes from the Friend's School Plant Sale.  They are giants.  They have taken my tomato cages that I inherited from the previous owner, laughed at their poor little wired frames, and tipped them over from their sheer girth.  I have had to resort to using bungee cords in my garden to keep the cages upright. Bungee cords!  Our neighbor's garden is on the other side of the fence (chain link) from ours.  They planted the same weekend we did.  Their tomatoes are just barely cresting over the tops of their cages.  

So I ask this, as a novice gardener, WTF is up with our garden?  Anyone?  Again, this garden is completely organic.  No fertilizers, pesticides, nuclear reactions, or performance enhancing drugs.  Just good old sun, water when I feel like it and occasional weeding.  And rabbit eating and dog trampling thrown in for good measure.  

Soon we will be buried in tomatoes.  We will have to eat our way out of the back door.