By seated you mean?
I'm thinking I should be pumping it up slowly, massaging the tyre as I go? Making sure it goes on evenly... this isn't standard practice though, is it?
A picture speaks a thousand words, rubez.
Post a couple of piccies so people can see what you're talking about and maybe offer meaningful advice.
Once seated let some air out.
The tube just stops air leaks, it has no structural strength.
What does that mean?
What causes wobbly tyres? (when you spin them, bike upside down) and the wheel itself is fine and doesn't waver.