Maybe it's just stress incontinence from having to pee and having been vigorously spinning, and it got triggered by the feeling of the tampon coming out. It's not uncommon for someone who has been 'holding it' for a while to have a little pee come out once they reach the toilet before they intend to release it deliberately, (that's stress incontinence). If you went to the bathroom after spin class, and figured that since you were on the loo you would change your tampon, if you also had to pee, the mechanical action of pulling it might have nudged your bladder to release a bit when you pulled the tampon.
I don't think you can urinate from your vagina. :>) Would you say this is watery discharge? That's considered normal most of the time. Exercise can increase interabdominal pressure. This can increase discharge as well as if it was indeed from your urethra (where urine comes from) urination. Some women use tampons for urine incontinence. Not that you do but that it does block all of that so removing it can perhaps result in a gush. I would not personally be concerned from what you write.