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No, it means that a person who entered Canada after June 24, 2020 will be ineligible to seek asylum if more than one year has passed from the date of their first entry after said date.
So if the person entered Canada before June 2020 will be eligible to seek asylum right
 
So if the person entered Canada before June 2020 will be eligible to seek asylum right
There is a condition to be eligible to seek asylum.

Asylum claims made more than one year after someone’s first entry into Canada after June 24, 2020, won’t be referred to the Immigration and Refugee Board of Canada (IRB),

Asylum claims made less than one year after someone’s first entry into Canada after June 24, 2020, will be referred to the Immigration and Refugee Board of Canada (IRB),
 
For example if you entered Canada after june 24, 2020 and made your claim within a year.
Your claim will be referred to IRB.
BUT
If you entered Canada after june 24, 2020 and made your claim after a year.

Your claim will not be referred to IRB.