Estaba ardiendo en dudas cuando una secretaria me invitó a seguirla por la misma puerta del fondo, hasta una oficina pequeña, con una larga estantería de gruesos volúmenes. Un beduino colosal se levantó en el escritorio del fondo y me estrechó la mano tuteándome con una efusión de viejo amigo. Hicimos juntos el bachillerato, me dijo, a modo de saludo.
From Gabriel García Márquez, "Memorias de mis putas tristes".
Translation:
I was burning with doubts when a secretary asked me to follow her through the same door in the rear, into a small office with long bookshelves that held thick volumes. A colossal Bedouin at a desk on the far side of the office stood and shook my hand, calling me _ tْ __ with the effusiveness of an old friend. We were in secondary school together, he said by way of greeting (Grossman).
I do not understand what the meaning of "tuteándome" in the first paragraph is, whereas the second one does not seem to give a clear translation of it. Any ideas?