I thought SPDs were originally intended as mountain bike clips, so there will always be play. the tension adjustment is just how tight the clip holds. In other words how much effort it takes to clip-in and clip-out. Once you're in, you'll still have the same amount of play, and shouldn't change how it feels...

I have SPD's on my cross bike, and works great... I have it on a pretty low/loose setting, and have never had accidental unclipping issues.