How do I know Plan B work if I took it on the 29 and I ovulate on the 1st?

There is no way of knowing whether emergency contraception will work.

Unless you're charting your fertility symptoms each day, or using an ovulation test, you may not know if you were definitely ovulating on 1st, neither. If you're relying on an app/website to tell you when you ovulate, they are just an estimate.

The only emergency contraceptive pill proven can prevent pregnancy during the 24 hours around ovulation, itself, is Ella (Ulipristal Acetate) (you can see that on their website), & even that is not guaranteed. Plan B might help at that time, but it has not been proven.

If you're close to ovulation, then Ella is probably a better option, for those reasons.

Hopefully you still had enough time for Plan B to prevent pregnancy. If you're ever that close to ovulation, & have an emergency, in future, then you might want to see if you can get the Ella pill, instead.

Another emergency measure, would have been to have a Paragard IUD fitted by a doctor, within 5 days/120 hours of the unprotected sex. That may prevent a pregnancy from implanting.