is it assur for one who keeps Rabeinu Tam zman (for motzaei shabbos) to ask a Jew who does not keep RT zman to do a melacha or derabanan for him?
Answer:
If a person keeps Rabbeinu Tam as a stringency, while accepting that according to the strict halachah one can be lenient to perform labor before this time, It is permitted to do this (to ask somebody for whom Shabbos has already terminated to perform melacha).
However, if Rabbinu Tam is kept as the full halachah, such that in principle this is what everybody should be doing, it is not permitted to ask others to perform labor.
Please see here for more details on this issue, and on the specific question see Shut Shevet HaLevi 1:53.
Best wishes.
