As to what was probably the intended meaning, I agree with #1. I read the sentence as defective, and suspect that the intent was to write,
For the period of time that any portion of the workers, with "workers" understood to include checkers, are working on commodity time [=with a commodity], all of them are to be listed as on commodity time.
But if this is a contract, it would be wise to ask to make sure, because the language is defective.
BTW, I would understand commodity here to mean cargo consisting of one specific good. I think the timekeeper is probably required to log the time the workers spend working with each specific commodity, rather than just time spent working with any of the cargo. Here, the entire team is always logged as on commodity time if any of them are (already or still) working with the cargo in question.