I think once the Riverlords knelt, there wasn’t much room for Edmure to do anything else – in addition to the very public statement that the Riverlords had just made about who they considered their king, there’s the fact that Robb has just very publicly saved the Riverlands, Riverrun, and Edmure himself from a humiliating defeat. For him to have backed out would have been seen as unbelievably, dishonorably, ungrateful.
But I don’t think it was the case that the Riverlords went first, either. Even before Greatjon stands up and acclaims Robb king, Edmure says “so you mean us to declare for Stannis?” – he’s already accepted Robb’s leadership as quid-pro-quo for his actions at the Whispering Woods and the Camps.