Atmosphere, also called mood, in a literary work is the emotional feeling created by the work from within the setting. It is a literary element and as such is a literary device common to all works of literature and requires description. Thus it does refer to the author's, narrator's or any character's state of mind. The other category of literary device is that of literary technique, which are techniques the writer may pick and choose from at will: e.g., sensory detail, symbolism, metaphor, personification, etc. Atmosphere is created by diction, setting, theme, description, dialog. Atmosphere is distinct from tone, which does refer to the narrator's state of mind.
"Tuition" refers to private teaching or instruction. In the short story "Private Tuition by Mr Bose" (not all English varieties employ a period following titles like "Mr" or "Dr"), the atmosphere is established in the first paragraph in which the gagging oppressive air is described. What begins as oppression and virtual strangulation builds in intensity as the story progresses leading to urges of violence then to urges arising from being taunted and ridiculed. This atmosphere continues even into the quiet and comfort of Bose's kitchen with his wife whom he loves and adores where she all but gags him with too many peace offerings in the way of the food she had been preparing during the private tutoring sessions.