The way the rules are written in general, I guess I don't feel like I can take anything for granted. I agree with your thoughts though.
The start of the Round is the most logical place for them to refresh. Under surprise it just says you can't take "actions", but you can make Defense Tests. If Defense Tests are free, then all is well. You basically just don't get your normal Action Allotment (which is probably how it should read instead). Kind of moot, I suppose. It's basically the same thing as getting it but not being able to spend it. You just couldn't do any type of spending of the Allotment until the start of the next round.
Surprise says :
"Those who fail this test also roll Initiative, but they cannot act or spend Edge in the first combat round. They still roll to defend against attacks and to soak damage, but they cannot take any actions on their own. Once that first combat round is over, they can act normally."
"Cannot take any actions" would seem to imply you can't spend any of your allotment, but doesn't specify. I suppose that's not a terribly relevant. If I can "roll to defend" though, can I spend a Minor to add an extra dice pool into the mix? I assume not? Per the Action section, that would be "an action" which I am forbidden from. This also better fits the idea of being surprised. Either way, if that's the read, it seems that as soon as the round goes back to the top of the order, you get your allotment (given/refreshed/unlocked) and can now take defense or anytime actions in response to attacks prior to your turn.