You're meant to restrict it when appropriate, yes.
The relevant part of the rules is just a little after your quote:
If you want to move more than one zone (up to anywhere else on the map), if a situation aspect suggests that it might be difficult to move freely, or if another character is in your way, then you must make an overcome action using ...
If there's a narrative reason which would tend to enforce any of the various possibilities, then that's what determines how you then play it out.
Fate isn't interested in dictating order. It's whatever makes narrative sense.
The Golden Rule (FC p. 185)
Decide what you’re trying to accomplish first, then consult the rules to help you do it.
I think the language is clear enough:
if there’s nothing preventing you from doing so, you can move one zone in addition to your action for the exchange.
"In addition", not "before" or "after". To me, this definitely means that you can move and act, or act and move, or even act while moving, whichever makes sense, given your specific ...
I tend to think that setting such pairings in stone tends to make the game boring. If Shoot is always opposed by Athletics (or whatever else you pick to replace it), then players justifiably tend to hog those two and all other skills are sidelined.
I believe the best way would be allowing creative use of the whole skill set, even allowing unorthodox choices ...
Have you found and read this review of an alpha version of the Kickstarter product?
I'll just go by your linked list of paradigms. The review appears to reveal that history in Fate of Cthulhu is either malleable or sensitive, and it describes the specific game mechanics which govern time travel in play.
As you play, you track [on the Timeline Sheet] the ...