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Hard to say with little detail on your rotation and gear. From my experience as others said practice of the fight helps a lot, but I saw no one really mention gear. Though we may not have official stat weights yet for RDM to work off, a single piece of gear being subpar for you could lead to lower numbers. Group composition, buffs use, and even yours and those you are doing run with mood can also as much play a factor. You of course can only control your own gear, rotation, and mood, but take a look at the group as a whole. It can play a lot into it as well.
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Isn't 3900 meant to be fairly good DPS at that iLv on SSS dummy, bearing in mind no party buffs etc etc? If not I'm doing something fairly wrong considering I'm i316 on my alt character. So I may post about this later after I do a rough recording of the rotation I'm using. Though some of this may be down to a little RNG, there's some occasions I'll pop out 3840, and others I'll pop out 3961 or so. The class as far as I can say is only easy in principle, but rather fairly difficult to actually execute.
In terms of reaction times, I just reorganised my hotbar and resized my UI and it made the world of difference.
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Most of it just comes down to practice. Take advantage of the 2.5sec between each dualcast to take a glance at your balance bar, procs and cd timers, then plan out your next 2-3 spells. After doing it for awhile and seeing the same patterns multiple times, it gets to the point you know what to do next almost without thinking.