Welcome and congrats.
No there shouldn't be any movement. It's a simple matter of tightening the mounting bolt on the top.
From memory on top of the shock there should be an allen key socket. You put an allen key into this to stop the shock from spinning as you are tightening the mounting bolt. Some shocks will, instead of an allen key have a flat section to use a spanner instead to hold it still.
The bolt should be tightened enough that there will be a slight bulge in the bushes.
https://teraflex.com/file/attachment...00861ff841.pdf