does purple conditioner work better if you apply it to dry hair and let it soak?

You should never mix a permanent toner with shampoo.  Only true semi direct dyes, like Manic Panic, Adore, Directions, etc.

I used to use purple shampoo to tone the yellow out of my base when I was pale pink, and five minutes in the shower was all I ever needed (even that was too much sometimes).  Other people will sit with toning shampoo under a shower cap for half an hour to get rid of brassiness or achieve silvery/ash blonde/white hair.  It really depends on quite a lot of variables--what shade your hair is, what shade you're trying to reach, your hair's porosity, the strength of the toner ... just do some strand tests and see what happens.  The worst that would happen is it would grab the colour and you may go lilac for a wash or two.