Does the application go to each consulting office separately at T1&T2?

I can only speak for McKinsey and it depends on if you are an experienced hire or University hire. I am assuming you are a University hire. If so, you rank your 3 offices and the recruiters send your resume to those 3 offices. The offices then select, in order, whether they want to extend an interview.

Let's say office 2 wants to interview you but office 1 did not. Each interviewer in round 1 (sometimes) receives a packet before your interview with your resume and your office preferences and reason. In round 2 (usually the final round), the interviewer will receive a packet with your resume, your office preferences and reason (this time for sure, not sometimes), your first round case performance sheets and your PEI performance sheets. So, everyone knows what offices you selected centrally and at the office level.