Good luck on your “interview day” next week!
Regarding your question, based on my personal experience, I would say it is not very common. In 4+ years I have never seen it happen at my previous company nor heard from other friends/colleagues in consulting (and other industries well). This not to say that it is bad whatsoever and actually getting back to candidates promptly usually is to be encouraged in my option, always considering to the extent that is possible that certain candidates may benefit from extra practice before each round. However, there is always usually at least a few days (sometimes weeks) gap between separate rounds as all the people within the company that are involved need at least some time to reflect on performance, come together and discuss next steps. This includes both discussing feedback sharing and for successful candidates scheduling / availability of interviewers for following round. The above can be time consuming, considering that normally in any organisation and particularly in consulting, people are busy and finding a time that works for everyone can be challenging already for discussing feedback (and even more so for coordinating subsequent rounds). Normally, in my experience, I have noticed very fast responses in highly dynamic / entrepreneurial organisations, which tend to have agile processes or in organisations that for any reason may require candidates to join quickly. However, this is not an absolute truth, as it may very well be that by design an organisation may want to choose to concentrate the interview rounds together (e.g. perhaps to accomodate partners that have particular / specific time availability for example). Regardless, in my experience, consulting companies tend to be quite transparent and clear upfront on what to expect at every stage of the interview process as this is already challenging on its own. Therefore, there shouldn't normally be, in my opinion, logistic / scheduling surprises, as everything should be promptly communicated upfront to the candidate.
So in short not very common in my experience and perhaps somewhat unusual but nothing to be particularly concerned about.
Hope it helps!