If this is a new solution, chances are that it wasn't completely blended when you measured it the first time. I'll let mine run for an hour or so with the air and water pumps stirring everything up real good before I get a reading I can trust.
In my exp, this is not the case. if the meter isn't broke, you should be able to get a reasonably close result day after day as long as the plants aren't drinking a good percentage of the water. Keep in mind that the plant uses the nutes and water so the readings shouldn't be the same, but after measuring for a few weeks, you should see a pattern.
especially with an ec that low i would not think it would be normal either. however with higher ex and large well established plants, i have not only seen the ec rise, but rise very very fast.
i had dwc toms my first time ever growing... they eventually drank like a gallon a day and would swing the ec very dramatically. you had to pretty much just add back tap or RO water because it was clear that they were consuming far more water than nutrients.
im not 100% why this is, but it definatly does happen.
on the other hand with my aero system, you would notice a very large drop in ec from the runoff water, when compared to the mist water.
my problem with the bad meter assumption is that they are so stupid simple to build, its hard to build a bad one. Ph meters are another issue entirely, but ec meters are very very simple devices and are not prone to wild fluctuation like that.
i am of corse assuming he is using a simple pen type... NOT the type with the two long metallic probes that you are supposed to put into the soil. those are IMO criminally bad, and are a joke.
he is also using citric acid which is a big problem, especially w/ respect to cost. citric acid is terrible for controlling PH in an alkalne solution because its entierly too weak.
its also an organic acid. from what i remember, the conjugate base of citric acid is vulnerable to all sorts of micro organisms, hence it is rapidly destroyed. some how the reaction is pushed back to the left, and further dissociation of the acid is suppressed via common ion effect. this is what i remember reading about. im not real sure about the specifics, as its been a long ass time since i read about it. citric acid is basically made in a bio reactor... while the specifics of said process is beyond me, its not hard to imagine why its not stable.
i would at least move to phosphoric acid, personally i use HCl from the pool store... costs me like 8 bucks a gallon, with a gallon lasting well over one year. keep in mind that i go through probably 1000-2000 gallons.