I think the ticks have always been somewhere hiding in your dog's coat and underneath the paws and that they got out of hiding because of the clipping and bathing. This is the case with my dog. They cannot remove the ticks at the shop because it will risk the spreading of the eggs and they will have ticks at their place. I bring my dog at the grooming shop every 3 months or when her fur is already too long because she always has the risk of tick infestation. I'd always request for her fur to be cut short so that I can easily remove the ticks. Surely enough, she'll have dead ticks sticking on her fur after grooming. There will be some that are still alive.
I usually scour her fur and her paws and I would see a lot of ticks in hiding so I remove them myself and drown them in water if she's not yet ready to be groomed. I bathe her myself every 4-5 days when the weather is too hot.