Eric, as I said, "aber" can have different functiosn within a sentence. If it is a conjunction, like "but" in English, you are right - it has to be at the beginning of the sentence (there are possibilities to put it a few positions later, but I won't go into that - just remember that German word order is not as strict as English word order).
However, in this sentence, "but" is not a conjunction, but a particle - "Abtönpartikel" in German. I don't know the complete terminus technicus in English, so I do not know how to adequately translate the "Abtön-" part, which is really important hier: it means that this word does not carry meaning or grammatical function, but only is a sort of "coloring" of the sentence ("abtönen" is a word for "making slight changes in color or tone"). It can stress a meaning (like in this example) or weaken the impact of a sentence, etc.
There are many Abtönpartikel in German (doch, so, aber, ja, ...), and they regularly vex foreigners and linguists alike.