I did use an alligator clip with a wire, as a heat sink. Wanted to be safe.
I soldered mine with the tabs facing down, so that minimal wire is exposed. I soldered mine before mounting the tweeter.
Mine also had a red dot next to the positive tab, albeit it's the larger tab. But, I too, thought that the phase gets switched somewhere in the crossover.
Here is my soldering tip for a novice, which I am. I was excited when it came to the soldering step and nearly didn't give the soldering iron time to fully warm up. Be patient and let it get hot, it makes things so much easier. And faster. You'll find you don't have to hold the iron on as long to get good results.