according to rav avraham yosef, it is permitted to make techina from techina paste on shabbat.
He states that the prohibition of Lisha (kneading) which making techina most resembles, is only when you take something that is not edible as is, and by adding another ingredient create an edible mixture. Therefore if you take mayonaise or ketchup and add to mashed potatoes, or to techina, since they are edible to begin there is no problem.
Others are of the opinion that there are issues with making techina on shabbos.
I know many people mix in a different way then regular when mixing techina (ie. if they normally stir clockwise, they will stir zig zag)
The gemara שבת קמ,א
"חרדל שלשוֹ מערב שבת, למחר ממחו בין ביד בין בכלי ונותן לתוכו דבש, ולא יטרוף אלא מערב"
Many understand that there is no Lisha (kneading) after it has been performed prior, and have the custom to mix the techina paste with a little water before shabbos and mix, allowing them to add whatever on shabbos.
The pri megadim understands that there is no lisha after lisha, and that is the case even when the originall lisha was done with the objects own juices, this is the case with techina paste, that it already underwent lisha before shabbos in the factory.
Additionally there is the idea that if by adding water/lemon juice etc, it becomes more liquidy (belila raka) then that is not called lisha