Here is my process. I till the plot (I have a 4’ tiller for my Kubota B2710). I spread the seed with a hand spreader (better control). I then drive on the seed bed with the tractor for good seed to soil contact. I generally plant clover/chicory and brassicas which are all very small seed.
Are you saying seed grows where the tire tracts are not, or the plot doesn’t grow at all? Are you getting enough moisture after planting?