How do I make Shimano SPD cleat lock into pedal more securely?
You're probably talking about "float", the way your foot rotates over the pedal. This is considered a feature, not a bug. There are different cleats you can get with different amounts of float; looking around, I do see there are "zero float" cleats that you can get for SPDs, and others with only 4° of float. The spring adjusts your release tension, not your float (I think).

After having ridden zero-float pedals for a long time, I'll take all the float I can get.