I've added map <F4> :!pdflatex % to my tex.vim. It's on demand, but after the first compilation it's almost instant. :) Edit: as mentioned in another comme

I've added map <F4> :!pdflatex % to my tex.vim. It's on demand, but after the first compilation it's almost instant. :) Edit: as mentioned in another comment, Evince updates automatically when the file changes.