Is it permissible to work for a jewelry company as a programmer for their website, knowing that the company used to operate on a system where the first customer received a percentage of the price of the product bought by the second customer they brought in, and that the company is determined to stop this practice?

The scenario mentioned in the question falls under the category of pyramid or multi-level marketing. Ruling on a matter is dependent on its true understanding. If the company ceases its illicit dealings, then there is no harm in working with it; otherwise, it is not permissible, due to the general meaning of Allah Almighty's saying: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression. And fear Allah; indeed, Allah is severe in penalty." And merely intending to abandon illicit dealings does not make it permissible to assist in them.