I got into the game in 2009 (Imperial Entanglements was the current set at the time), and 1 activation was already a DCI rule by that time. When WotC discontinued the game, this site (swmgamers.com) took over the job of keeping the game alive. As it turns out, bloomilk.com has a great squadbuilder and database of the pieces, so it gets far more traffic and still has active forums. This site still holds the official documentation, though, and this is where the Vsets* are designed (in hidden forums).
Here is the page with the rules:
http://swmgamers.com/SWM/SWM%20Rules%20Main.htmlThe top left margin of that page (if you're viewing on a desktop) has the final official documentation from WotC. I don't have a copy of the floor rules from end-of-WotC era, but you can find the current** floor rules there as the first link under "Tournament Information". The vast majority of the current floor rules are still carried over from the WotC-era (aka DCI) floor rules. The rule in question is under "615. Tournament Play Procedures" under the paragraph labeled "Number of Activations per Round". The wording for that rule hasn't changed since the DCI floor rules 10 years ago.
The floor rules change would have been originally announced on the official WotC forums, which are now defunct. There certainly would have been discussion about it here as well - a search might turn up the original discussion. It would have been between 2006 and 2008, I guess.
Note that the "1 activation in the first round" rule is only a floor rule. The official rule for non-tournament play is still the same 2 activations per round, including round 1. However, pretty much everyone active in the SWMinis community uses the tournament rule even for casual play.
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* Vsets are new stat cards that can be used with the original WotC miniatures or with custom miniatures that players create. New Vsets have been produced twice per year ever since the game was discontinued. VSet #20 was just released last month
** The floor rules change very little over time - usually just 1 or 2 notes/minor changes per year plus a change to the maplist. Sometimes no changes at all. Recently updates have just been an announcement in the bloomilk forums. I just realized it's been 5 years since we had a full writeup of the floor rules document. It's about time we updated the main document to include the last few incremental changes. Most of those changes relate to Vset errata, found in the document just below the floor rules (Post-WotC Errata and Balance Committee Rulings).