Despite the burgeoning research on feedback, we know little about the ways in which students engage with supervisory feedback in doctoral writing -- a crucial element for understanding students' feedback uptake. To address this issue, this study uses text analysis and semi-structured interviews to explore Chinese international doctoral students' engagement with supervisory feedback from invisible and overt dimensions [Handley, Karen, Margaret Price, and Jill Millar. 2011. "Beyond 'Doing Time': Investigating the Concept of Student Engagement with Feedback." "Oxford Review of Education" 37 (4): 543-560]. We contextualise this study within intercultural doctoral supervision and focus on the process of students' writing and revising their PhD proposals. Results show that by engaging invisibly and overtly with the feedback, the students not only co-construct and lead the feedback dialogues but also maintain their voice and ownership of the writing. However, the findings also suggest the danger that supervisors may neglect students' invisible feedback engagement and interpret their mindful reflections as none or superficial engagement with feedback. Students' feedback engagement involves negotiations with multiple, even conflicting cultural values mainly from disciplinary norms and their inherited Chinese cultures (e.g. the different manifestations of critical thinking). We suggest developing a constructive attitude towards cultural diversity to facilitate feedback dialogues in intercultural doctoral supervision.