The adverb for presumptuous: you do the thing in a way that assumes a right you do not have, and it comes across as rude. Someone who presumptuously sits in the teacher’s chair, or presumptuously answers for a person who was not asked, has stepped over a line. It is a little formal; in easy talk people often say rudely, or just describe the act. Same warning as the adjective: this is manners, not “based on a likely belief.”