Attorneys know that it is inappropriate to put the court reporter in the middle of their legal wranglings with opposing counsel, and therefore, generally upon hearing this statement by the reporter, they will accept it and move forward. Typically, the person who wanted to remain on the record will make their statement, followed by the person who wanted to go off the record adding comments about the appropriateness of those statements; perhaps even asking a judge to consider striking the contested remarks. This would happen at a later date, and it would have nothing to do with you. The reporter should continue capturing all remarks and testimony unless and until all agree to go off the record or to conclude the proceedings.
Be aware that the objecting party may request that the court reporter “certify” the contested part of the transcript, or note it in the transcript index. It is appropriate to agree to do this.