Now that I've gotten all the secrets I can finally answer this question.
In principal no. You do not need to revisit missions to get all the secrets. You just need keen eyes as you go through the levels. Most secrets require just some platforming to get to, but some also require hitting certain switches or pulling levers and these tend to be hidden.
The later missions start to have numerous points of no return that do prevent you from going back to earlier parts of the map. These can prevent you from getting to some of the secrets you missed earlier.
Also, the double jump you get in the 5th mission, the Argent Tower, makes traversing the earlier maps much less of a pain, so it's easier to get the secrets you missed.