Since you have not stated any jurisdiction in your question, I am basing this answer on the EU, which is what I am familiar with. Rules in many other parts of the world are going to be similar if not nearly identical.
Regulation EU 376/2014 lays down rules on the reporting, analysis and follow-up of occurrences in civil aviation. On the list of Mandatory Reporting you will find:
(v) communication-related occurrences;
which I think, among the possible categories, would be the best fit for the kind of event you describe. However, it is not detailed further what is encompassed by this category, so whether something like what you describe falls under mandatory reporting, I don't know for sure. In theory, rules were violated (unrelated chatter on the radio is, quite simply, not allowed). In practise, it doesn't sound like any harm was done.
In any case, there is also Voluntary Reporting, which is designed to capture
(a) details of occurrences that may not be captured by the mandatory reporting system;
(b) other safety-related information which is perceived by the reporter as an actual or potential hazard to aviation safety.
The rules concerning reporting can be quite difficult to comprehend; my general advice (and what I have learned at school) is: if in doubt, file a report. If you feel the safe environment was in any way compromised, you should report it. Remember, the aim of a report is not to appoint blame, but rather to improve safety. I know from experience that it might be difficult to report something done by someone you know, since it might feel like you are pointing fingers or ratting someone out, but the truth is that the reason aviation is so safe, is because the people who work with aviation takes safety seriously, and reports violations.
As for whether the controller is going to report your situation, I doubt it - they is the one who initiated in the first place after all. But again, if you feel safety was violated, please write a report. Your writing today may save lives tomorrow.
