To the OP: I'm guessing that you were satisfied after completing the power checks prior to departure, and that the mag drops were within limits. Assuming this to be so, the fault that you later diagnosed (loss of one mag) would surely have only led to a relatively small reduction of RPM - perhaps no more than 200 with max power selected?
I'm assuming that the reduced ROC was due to the natural instinct of your student (or perhaps you) to pitch down, and the VSI reflected this with the indications you quote. Nevertheless the aircraft had sufficient power to maintain a safe climb, and you were in the immediate vicinity of the aerodrome. I think that a PAN call was appropriate, but as to whether you as instructor should have taken immediate control is debatable and depends on a number of factors, not least of which is your experience as an instructor and the confidence you have in knowing the limits of your abilities.
The absolute safest course of action was that which you chose. As instructor you were not only the P1, but your level experience and qualifications indicate that you were the safer and more current pair of hands to deal with the issue. As instructors though our function is to teach skills, and these are best taught with supervised practice. As Ascend Charlie pointed out, "you tell me, I forget - you show me, I might remember, and you let me do it, I learn." As students master new skills their confidence is boosted, and this propels the learning process.
As instructors we often allow students to deal with abnormal situations. A ballooned landing is a good example of something that has gone wrong that needs to be corrected in the appropriate way, and with a degree of haste. A junior instructor will have less confidence in his ability to correct the balloon if the student fails to act quickly, whereas a seasoned teacher is likely to give the student more time to fix something he needs to learn to deal with. A rough or partially running engine is not an entirely different matter, especially when the student has been taught emergencies of this nature previously.
I think it would be unfair of anyone to criticize you for handling the airplane yourself as only you know the full circumstances, weather etc. You didn't tell us though whether you let him/her carry out the approach and landing once you had attained a safe height and dealt with the RT. Glad all ended well!