Tosfos (Sukkah 35) writes that tevel is chayav in challah only if there is sufficient volume of dough to be chayav after terumos and ma'asros are removed. Since terumos and ma'asros belong to the kohein and levi, that portion of dough does not count as "arisoseichem". However, the Ras"h disagrees and holds that tevel is chayav based on the total volume of the dough without subtracting terumos and ma'asros.
The Minchas Chinuch (385) questions Tosfos' view. Dough which is owned in partnership by two people is chayav in challah and is considered "arisoseichem" even if each partner's portion is less the size which would be chayav in challah. Why is tevel different? Even if the kohein and levi "own" a portion of dough because of their terumos and ma'asros claim, the dough as a whole should still be considered "arisoseichem"?
R' Shmuel Rozofski z"l answers: the problem of a partnership is each party does not own a sufficient quantity of dough. In that case we say ownership of a part creates responsibility for the whole; therefore, dough is "arisoseichem". However, tevel poses a problem not just of quantity, but also of what is owned. Terumah is exempt from challah and therefore exempts the dough which it is part of from obligation.
The dispute between the Ras"h and Tosfos can be formulated in this way: does the terumah portion of tevel represent just a lack of quantity or is it an inherent exemption?