As you are referring to a graph, where the lines are physically drawn on a piece of paper (or on a computer screen or whatever), there is clearly a "where", the place on the graph where the lines begin going up. So "somewhere between 2006 and 2010" is perfectly acceptable and is literally accurate. There is a place on the graph between the place marked 2006 and the place marked 2010, etc.
If you were just talking of this trend generally, without reference to a graph, it would be more correct to say "some time between". But people often do say "somewhere between" in that context. Perhaps they are thinking of a graph or perhaps their language is just getting a little sloppy.
BTW "first three lines" requires an article. It should be "THE first three lines". And we don't say that a trend "raises", we say that it "rises". So the sentence should be, "Somewhere between 2006 and 2010, the first three lines rise significantly."