I remember taking a colleague for his first flight, an L4 Cub. The weather was not great,bit windy, and he told me years later that he had been terrified. I had not realised, I thought he had enjoyed it
I have a fair number of hours in vintage taildraggers, and most vintage taildraggers do not have a stall warner.
I would be concerned at the stall warner going off on base leg in any type. In fact, I do not like to hear the sound of stall warner at any stage. My colleague, mentioned above, habitually flares too early, and the stall warner kicks in. I tactfully try and modify this approach, however, it is the way he continues to fly
The event mentioned by the poster does not mention approach conditions, however, if the base leg was flown into wind, and a warner sounded, then he was too slow, and not reading the flight conditions, in which case he should get some additional training/hours on type, and you should not go up again until confident that he can cope.