issur terumah and kedushas terumah

Rashi in Yevamos (86a) writes that the issur of tevel occurs because terumah is mixed into the food and terumah is not allowed to be eaten מה תרומה טובלת. שכל זמן שלא הופרשה חייבין מיתה על אכילתו של טבל דהא מיתה כתיב ביה: 

Tos asks: if Rashi is correct, then a kohen should be allowed to eat tevel, since a kohen can eat terumah.  Since that is not the case, we see that tevel is an independent issur, not just a result of not having terumah yet removed.   ופי' ריב"ן משו' דדרשי' בפ' הנשרפין (סנהדרין פג. ושם) ולא יחללו את קדשי בני ישראל אשר ירימו בעתידים לתרום הכתוב מדבר ויליף חילול (א) מתרומה:

R' Wahrman z"l suggests (inyanaim ketzarim siman 4 in the back of She'eiris Yosef vol 3, see also vol 2 siman 47) that there are two dinim in terumah: there is 1) the issur termunah, i.e. terumah cannot be eaten by just anybody; 2) and there is kedushas terumah -- terumah requires shemira, it has specific dinim with regards to tumah and taharah, someone who eats it b'shogeg pays an additional 1/5 penalty, etc.  

Perhaps tevel is prohibited because the the issur terumah is inherent in the mixture, as Rashi writes, but the kedushas terumah does not kick in until after hafrashas terumah, and therefore, since there is not yet kedushas terumah, tevel cannot be eaten by a kohen.