"crafty steampunk skill lines that grow more powerful as your craft skills increase" "Tinkering, Wandcrafting and Alchemy will improve your scientific attacks." What exactly is scaled? Does this affect basic attacks?
No, it doesn't affect the basic attack. And only skills are scaled. A fine example is Clockwork Knight - some of its skills scale with tinkering. Wands also get more powerful based on your wandcrafting skill. And if you want to know what scales with that exactly, then you have to take a look at the code, or experiment in the game.
Rocket jump from CK scales with tinkering. Baromatic pulse device and barometic vortex upgrade from rogue scientist scales with tinkering. Acidical projector and gas cannister from rogue scientist scales with alchemy. Aethereal death ray from rogue scientist scales (heavily) with wandcrafting.
Rocket Jump and Charge of the Steam Brigade do scale with tinkering but in a rather complicated way (the damage at the site you launch from is what gets scaled to tinkering, armor absorption matters at the target site).