Have had that happen twice. Once with Paris (ex-Old Compton St walkup) when she was an indy (actually the condom came off inside her rather than breaking) and once with a Hungarian masseuse where the issue was probably a bad combination of latex and massage oil.
Tbh it didn’t phase me that much. WGs that look after themselves are less likely to be carrying an STD than a Friday night civvie hookup. I just got tested after the appropriate passage of time and got the all clear.
Oh yeah, I wasn't worried about catching anything, neither was the WG, we were both concerned she would fall pregnant. Thankfully she managed to get a morning after pill the day after and the next time I saw her, approx. a month later as she went on a uni trip a day or two after that shift, the first thing she did was kiss me and tell me; 'don't worry, I got my period last week'.
Since then I bring my own, larger condoms to meets as regular ones are too tight and uncomfortable and I have broken a few. Seriously if you find regular condoms to be too big/too small, find some that fit you comfortably. It could be the difference between you catching something if it slips off/breaks or even an unwanted pregnancy!