I have just changed my shock spring from a 350lb 2.25 to a 500lb 2.25. I noticed the 500lb is slightly shorter, but other than that when I tighten the top part onto the coil spring it holds it but you can move the spring slightly from side to side.

Is this normal?
Or
Do I need to get a bigger top part for the coil to sit on?

Yes, that’s normal. And no you don’t need to change anything, as soon as you sit on the bike, the force that the spring exerts on the collar is so high (probably nearly 300lbs just with you sitting on the bike, near 1/2 ton at full travel) that friction will prevent it moving side to side.