The vet is right , but he missed telling you to supervise her closelly throught the first few days, when i have a c-section like this i set ready to be up all night and all day , the second night you may take naps.
She may kill the puppies if she pushes them away, they may get cold and die if they are away from mom's body heat , also they need to nurse almost non-stop for that nice colostrum and with them nursing the oxitocine will be produced, that is the hormone that will cause her natural instincts to come alive and love the puppies. It sounds like all is good but you really need to be checking her and puppies non-stop for this first night ... do you have a heating pad there to keep things warm? I always use one after any delivery , specially c-sections. Make sure she is eating well too, i like to use "a/d" after c-sections , it gives them plenty of nutrients and it is easy to digest after surgery ... after the milk really comes down and she is liking the puppies to potty and staying with them without having to be locked up , you will be fine to rest.
It sounds like all is going well... just a lot more homework when you have a c-section... Just brew a huge carafe of coffee and enjoy ... all will be well
Congrats !!!!
XOXO