'non-' originates from Latin, specifically the word 'non', where 'non' meant 'not'. 'alumni' originates from Latin, specifically the word 'alumnus', where 'alumnus' meant 'foster son' or 'pupil'. 'related' originates from Latin, specifically the past participle 'relatus' (from 'referre' / 'ferre'), where the element meant 'brought' or 'carried' (through 're-' + 'ferre').

'alumnus' entered English from Latin via Medieval and early modern scholarly usage and formed the plural 'alumni' in Latin; 'related' developed from Latin 'relatus' through Old French 'relater' into Middle English 'relaten', becoming Modern English 'relate' and its past participle 'related'; the prefix 'non-' was used in Latin and Old English compounds and continued as a productive negating prefix in Modern English, forming compounds like 'non-alumni-related'.

Initially, the components meant 'not' (for 'non-'), 'foster son/pupil' (for 'alumnus'), and 'brought/connected' (for 'relatus'); over time they combined to form the compound adjective meaning 'not connected to or concerning alumni'.