Here is the little I could glean from the literature about the actual tasks of the cellarius. Celarii are mentioned frequently enough in texts but there is very little about their tasks, unfortunately.
heating up the wine
(for all of the above see: Plautus, Miles Gloriosus, act 3, scene 2)
doctoring wine to hide ...
It's Late Latin. From the OED:
Originally this governed a following word in the genitive, but in late Latin the tendency to use the phrase as a compound noun appears in vicequæstor (equivalent to prōquæstor of analogous origin). In medieval Latin such formations became common, as vicecomes, -consul, -decanus, -dominus, -princeps, -rector, -rex, etc.
For 'entrepreneur', or even 'businessman', just as in English, there are few words in Latin of such broad meaning. With the senatorial ranks officially forbidden to engage in commerce, it was left to the equestrians, who were content to manage business both for themselves and for others. Within the equestrian order there seem to have been two broad ...
Traupman's book is great for a lot of things, but there are some things he seems just to have made up (as far as I can tell), and administer, minister seem to be among them. I think there's a sense of the subordinate in those words that doesn't mesh well with the meaning you're looking for. I'd go with præfectus here—
—unless you wanted to use archon, which ...
In a smaller restaurant, caupo would be very appropriate, particularly if it's a family business. Another word which was certainly used in Antiquity was simply puer (see Sense B.2 in L&S).
But if we were to use a term to describe the job out of context (say, writing it in a curriculum vitae, for instance) I'd probably go for dapifer as you wrote.
According to this dictionary or this one, both are translated by prælector.
Lewis&Short gives then this definition of prælector:
praelector, ōris, m. id., one who reads an author to others and adds explanations, a prelector (post-class.; cf.: lector, recitator), Gell. 18, 5, 6.
Cassel's dictionary proposes scholasticus as a lecturer in the schools, ...
Minister somehow doesn't quite fit the case: its primary meanings imply subservience. A better word would, I think, be praepositivus, which better indicates someone put in charge.
This kind of thing is always a bit unsatisfactory in the result. Princeps minister, which you quote, doesn't seem quite right, either, even though, in context, the meaning should ...
In Italy, quoting the website of the European University Institute,
apart from ‘assegno di ricerca’, ‘professore a contratto’, and ‘ricercatore di tipo B’, all other positions are tenure or tenure-track.
In particular any position of Associate Professor (‘professore associato’) is a tenure-track or tenured one, and that of Full Professor (‘professore ...
Central-European have a similar concept where the important step is a habilitation. habilitatio (medieval) - making qualified or eligible, declaratio habilitatis - declaration of qualification. After a habilitation one becomes a docent - docens - teaching (a lecturer).
To make sure the word is understood correctly as referring to the academic concept of tenure, I suggest taking a word that is easily connected to the English "tenure".
My suggestion is tentura, "holding" (roughly), from the past participle tentus of tenere, "to hold, master, guard, or stay".
I think this captures the idea quite nicely is easy to recognize.
I found an attestation of the title professor auxiliaris:
Antonius Toledo, Iuris in Universitate Professor Auxiliaris.
See page 4 (= 286) of this file.
The support for this translation is somewhat weak, but I don't see a better option.
Googling reveals several uses of professor associatus in Vicipaedia and some other sources.
This is also supported by ...