Steve that sounds excellent.
Yes I recommend you tamp down the compost. At times like this when it’s so dry, and the compost is unlikely to be saturated with moisture, it is much better that you firm it. Even by walking on it when the compost is rather dry, as you will see me do (I think, depends on editing) on Gardeners World this Friday.
It’s difficult to compact compost, and firm compost gives better anchorage to plant roots.
Older beds (i.e. not freshly created) do not need firming like this, just brand new ones.
