LED strip flash to music
If I understand you correctly, you just need to convert the amplitude of the music to the brightness of the LEDs. First, note that human perception of sound is actually very skewed and tends to follow a logarithmic curve. As a result, what you understand to be 70% volume is likely much different than if you were to look at the percentage of the "100% volume" in absolute air pressure.

Moving on from that, your circuit (the original one), seems to be alright. In theory, the voltage across your transistor will be pretty low. You are likely to stay in the saturation region of the transistor (left of the dashed blue line in this diagram.

What this means is that the current through your LEDs will be limited by the transistor in a more-or-less linear way. This could be solved for with a load line (for which I refer you here, since it's not really necessary).

Given your LED strip is spec'd at 12V, I recommend powering it with 12V. The reason is that the forward drop on the LED effectively lowers the voltage available to generate current, and the LEDs likely require &lt;25mA of current. For example, a 5V source with an LED that has a forward drop of 2.2V and a current-limiting resistor of 220R will have 

(5 - 2.2) / 220 = 0.0127 -&gt; 12.7mA


which is a reasonable amount of current. Hopefully that demonstrates why 12V might be necessary for the strip. Looking again at your question, you may be providing the strip with 12V (and only limiting the LM386 to 5V, but I wanted to make sure). Going to your point that low frequency sounds tend to make it light up more, the human ear actually perceives loudness differently across the audio spectrum. Sounds ~1kHz tend to be the loudest to us even if the absolute air pressure is the same as for a different frequency. The reaction you see might just be due to our distorted perception.

Now, as I said before, the transistor will limit the current available to the LEDs based on its base current. The LM386 can tolerate 12V. It's spec'd in the datasheet, and I doubt you'll find heat problems. I am assuming that you're using the LM386 to drive the transistor, and if you are, then you should place a current limiting resistor between the output of the LM386 and the base of the transistor. You can see here, that the base current is limited to 5mA, and a good transistor will permit a current multiplication of at least 10x, so it should allow a max current of 50mA minimum. Now, Imagine that your supply is changing, so it isn't just 5V. That's your audio signal. As a result, anything larger than 5V will cause more current to flow. Lower voltages will cause less.

However, to make sure this works (since audio is an AC signal), you have to make sure the voltage is never negative, otherwise you'll only ever get the LEDs to light up half of the time. That's slightly more complicated, and you might be getting a DC offset signal anyway.

As for the document you linked to, it shows the same configuration that I think almost every other BJT/FET uses (at least for a TO220). It is almost always Base/Collector/Emitter (or Gate/Drain/Source). I'm not entirely sure what you are getting at with 


  input/output/ground


but the first diagram you have seems to be correct.

Hopefully all of that info helps. I'd like to add that if I were doing this, I would take the signal, pass it through an op amp (which can provide a 30mA constant current source) which drives an NPN BJT in a low-side drive configuration. I am assuming you want to design/build it yourself, so I won't link a schematic unless you ask for one.

Good luck!