Those born, raised and educated in Asia may naturally tend to deflect focus from themselves because of a cultural background that emphasizes the community over the individual. If that's the case for you, you'll need to be aware of this tendency and overcome it, since it's critical to articulate yourself forcefully during the fit component of the interview process. You're marketing yourself during the interview -- remember that it is often the only period of time (and a short period, at that) when you have a formal opportunity to convince prospective employers that you're suitable for the role.
Even though it is important to be perceived as an excellent team player, the interviewer is more interested in what you, specifically, have achieved. Many Asian applicants were raised in cultures where the community takes precedence over the individual, and may be reluctant to "toot their own horn." Remember that the consulting firms are planning to hire you, not your entire team, and they want to see initiative and leadership from you.
If you're asked to talk about a specific aspect of your school or work experience, make sure to emphasize actions and outcomes. In addition, if the interviewer is clearly not from your country, which will happen at least half the time, you may feel you have to make sure he or she understands any specific local context or nuances in your examples. But don't fall into the trap of spending too much time explaining detailed local context and nuances; a brief synopsis of the situation should be sufficient, as the consultants will quickly understand ambiguous contexts.
For example, when you talk about how you led your club to raise $100K in funding through a campaign, focus on what you did and the positive outcome, rather than going into a lengthy explanation as to why there was this need to raise the fund.
Try to have a range of examples on hand focusing on your analytical, leadership, teamwork and interpersonal abilities. The examples should be communicated in a concise and crisp manner, with sufficient details focusing on the specific actions you took, and the positive outcome that occurred.
The nature and structure of "fit" interviews held in Asian offices of consulting firms are broadly similar to those conducted in North America and European offices. Specifically, all interviewers look for similar attributes like analytical and interpersonal abilities, leadership, and fit with the company's culture and values.