The rules say the following about initiative:
Once the cards are dealt, the Game Master starts the round by counting down from the Ace to the Deuce, with each group resolving its actions when its card comes up.
However as you noted, there is a bit of ambiguity as to when the actions are declared. Are they declared before their card comes up or when the card comes up?
At Origins one year, I played in a game run by Shane Lacy Hensley, the creator of Savage Worlds. He did it the way that I think most players do it: when your card comes up, you declare what your action is (which may not have been the one you intended when the cards were dealt) and then resolve any rolls. In other words, your action is declared not when the cards are dealt, but when your card comes up in initiative.
Part of the reasoning behind this is especially in large battles it's hard to keep track of everyone's actions. Imagine if there were a large battle with 15 combatants. If everyone had to determine cards right as they were dealt, I'm sure that someone down the line would forget what they had intended to do (not to mention they might not be honest about it). It's much easier to just have everyone pick actions as they come up.
Given that this is how the creator of Savage Worlds does it, I think it's clear that this is definitely how the rules are intended to work.