Steve, I'm not sure I follow you. Tape is a proper means of insulation, and it's certainly applied 'after' the splice is made. I don't have any problem with heat shrink tube as covering for a splice.
I would have a problem is the tube was left with an open end. Otherwise, use it.
For the mechanical connection, twisting the wires is generally enough. Sure, there are exceptions ... where you need to use a hydraulically crimped or welded connection ... but for most purposes, twisting is plenty good.
Naturally, for larger wire (like you might see used in a service), the practice is not to simply try to twist the wires, but rather to braid the strands together. There's an entire art to these splices, that's pretty much been lost.
