Rabbeinu Tam permitted one to hire workers בקבלנות, which means they are paid for the job and not encouraged to work on shabbos. Tosafos writes that he proves his heter from our mishna. Just as one is allowed to give hides to a tanner knowing that he will tan the hides on shabbos, so long as he doesn't need to tan them on shabbos, similarly one can hire gentile workers who will be working on shabbos so long as they can choose not to work on shabbos. The issur of hiring workers is technically only if you are hiring them to work on shabbos, but if you hire them to do the job at their convenience and they choose to work on shabbos, that is not a problem. However, Tosafos rejects Rabbeinu Tam because whenever the goy is working on the Jews property and doing construction, it is a very public activity and people are unaware of the deal and will assume that he hired the workers by the hour to work on Shabbos. Tosafos concludes that even Rabbeinu Tam when he built his house, would not allow the workers to actually work on shabbos.
Rav Moshe (Igros Moshe 4:52) discusses a situation where a hotel owner hires a Jewish contractor who has non-jewish employees. The owner of the hotel is religious, but the contractor is not and doesn't really care about the nuances of the halacha. However, if the owner of the hotel would not allow the work to take place on shabbos, the contractor is not willing to guarantee the job. Rav Moshe writes that nowadays it is very common for property owners to hire out contractors who are paid for the job and not by the hour, therefore even according to Tosafos, the concern of people thinking that he hired the workers by the hour doesn't apply. It is similar to a field which is normal to be done using arisus, and therefore permitted (as Tosafos Yeshanim brings). However, if the work is going to be done 7 days a week so that the Jewish hotel owner is actually benefiting from it being done on shabbos, it is assur. But, if the workers are going to work on shabbos and take off sunday, since they could just as easily work on sunday and take off on shabbos, it is mutar. This is all from the perspective of the hotel owner, but from the perspective of the contractor, even if he agrees to hire the workers by the job and not pay them by the hour, it is still a problem since it is very normal for contractors to hire by the hour, and therefore the ma'aris ayin problem of Tosafos applies. Therefore, the only approach to allow this would be for the contractor to sell the business on shabbos to his workers, which Rav Moshe is not happy about - קשה לעשות בדור פרוץ כזה וגם מפורסם שהוא של ישראל.