Grammar Geek“So possibly this ("on the minute") usage is common elsewhere.”
I think GG's right; "on the Xth minute" doesn't sound unusual to me, and there are several examples on the BBC website, e.g.
1. Harry Kewell did pull back a controversial goal for Leeds on the 80th minute, much to the fury of Strachan.
2. Rudd latched onto the mistake and simply walked the ball into the net, capping his hat-trick on the 79th minute
3. After three consecutive corners resulted in a headed goal from Rudd on the 64th minute, the rout was on
(I have always understood it as "at the beginning of the Xth minute", as in "on the stroke of midnight"; though on reflection I doubt whether commentators intend that kind of precision.)
Best wishes,
MrP