Halacha forbids performing Melacha (activity forbidden on Shabbat) on Saturday night, even after Shabbat has concluded, until one has made a verbal declaration formally ending the Shabbat observance. Meaning, one may not perform Melacha on Mosa’eh Shabbat until he recites Habdala, recites the words, "Baruch Ha’mabdil Ben Kodesh Le’hol," or recites "Ata Honantanu" in Arbit. A person who did not make any such recitation is forbidden from doing Melacha through Tuesday. The prohibition does not extend into Wednesday, since at that point the week becomes associated with the coming Shabbat, as opposed to the previous Shabbat.
An interesting question arises as to whether one may hire the services of a non-observant Jew who presumably has not recited Habdala (or the other recitations mentioned above) since the previous Shabbat. For example, may a person hire a non-observant taxi driver to drive him somewhere on Mosa’eh Shabbat, Sunday, Monday or Tuesday? Seemingly, since it is forbidden for the driver to perform Melacha through Tuesday, it would be forbidden to hire him to perform Melacha on one’s behalf. For that matter, may an employer hire a Jewish worker who does not observe Shabbat and thus, in all likelihood, does not recite Habdala, and is therefore forbidden from performing Melacha from Mosa’eh Shabbat through Tuesday?
This question was addressed by Rabbi Eliezer Waldenberg (Israel, 1915-2006), in his work Sitz Eliezer. He cites some authorities who advise a person in this situation to extend the wish of "Shabua Tob" ("Have a good week") to the non-observant Jew, so that he will then respond, "Shabua Tob." This response, according to some views, qualifies as a formal declaration of the end of Shabbat, and thus suffices to permit one to perform Melacha. Thus, for example, a person who takes a taxi driven by a non-observant Jew should wish the driver "Shabua Tob" before entering the car, so that the driver will respond and then be allowed to perform Melacha.
Rav Waldenberg himself, however, disagrees with this view, noting that the "Shabua Tov" greeting does not relate in any way to the theme of Habdala, the distinction between Shabbat and the weekday. In his view, wishing somebody "Have a good week" does not suffice to permit one to perform Melacha.
After a lengthy and thorough analysis of this issue, Rabbi Waldenberg concludes that it is permissible to hire a non-observant Jew who did not recite Habdala, though for an entirely different reason. Rabbi Waldenberg establishes that the prohibition against performing Melacha before reciting Habdala applies only to somebody who intends to recite Habdala. If a person does not observe the Misvot and therefore does not plan on reciting Habdala, then although he is certainly guilty of neglecting a Misva, he is not bound by the prohibition against performing Melacha after Shabbat. Since he does not anticipate reciting Habdala, his failure to do so has no effect upon his status with respect to Melacha after Shabbat. Rav Waldenberg draws an analogy to the prohibition against eating in the morning before reciting Shaharit. Despite this prohibition, it is permissible to serve breakfast to a non-observant Jew who can be presumed not to have prayed Shaharit that morning. Since the non-observant Jew has no intention of praying Shaharit, the prohibition against eating before praying does not pertain to him. Similarly, Rav Waldenberg asserts, a person who does not plan on reciting Habdala is not included in the prohibition against performing Melacha before Habdala, and one may therefore hire his services even though he has not recited Habdala.
Summary: Although one may not perform Melacha after Shabbat before he recites Habdala (or some other formal declaration of the end of Shabbat), it is permissible to hire the services of a non-observant Jew, even though he can be presumed not to have recited Habdala.