Smart parking don't have anything to do with ASDA and operate independently, but ASDA will have brought them in
There are signs around the site warning people of the £70 charge if they are seen leaving the site on foot, and I have seen wardens patrolling the car park looking for people - but I would argue that it's an unenforceable rule (how do you prove which person is associated to which car?)
I only ever park there if I'm planning on going into Asda, but I may also pop into town as well - if they stop me from doing that, I'll just go and park at Sainsbury's, get my bits of shopping from there instead, claim my car park charge back then head into town.