One can also look at Word Reference if there is confusion: wordreference.com In this instance their explanation of the reflexive verb "tenersi" UNDER THE COLLINS (dictionary) TAB shows that tenersi means "to hold onto." http://www.wordreference.com/iten/tenere and reflexive verbs always take "essere" as the auxiliary.
I'm not an expert of English language, but I think that "to himself" is redundant, and it's good if you want to highligth that the professor uses the key only for himself and doesn't share it. If it is so the Italian translation would be "il professore si è tenuto la chiave PER SE".
In the informal language "tenere" and "tenersi" are sinonimous and they mean only "keep": "il professore ha tenuto la chiave" = "il professore si è tenuto la chiave" different forms, the same meaning
Indeed this is not a reflexive verb. He does not "hold himself (tenersi) to something". He "keeps something to/for himself".
The "si" in this sentence is a "si enclitico".
See http://www.treccani.it/enciclopedia/parole-enclitiche_%28Enciclopedia_dell%27Italiano%29/, point 4.
I realized that that was not the best of all explanations. This a better one for the use of verbi pronominali (point 2.3): http://www.treccani.it/enciclopedia/verbi-pronominali_(Enciclopedia_dell'Italiano)/