Is it obligatory for me to pay an additional amount to someone with whom I had agreed upon a specific task, and then, after its completion, he demanded a much larger sum than the usual wage?

If a man prepares himself to work for you and for others, he is entitled to a wage equivalent to that of his peers ( اجر المثل). If he does not prepare himself, then he must reach a settlement with you. This should be a lesson for you in dealing with people: do not engage in any dealings except after knowing the agreement.