Right of tenant to refuse rent increase after serving a legal notice

When there were more than 90 days, I sent an email to the tenant that I want to increase the rent which was higher than what was mentioned in the rental index.

The tenant replied to me saying they don't want to renew the rental contract. Now when there is less than a month left in contract expiration, I got an email from them that the contract will renew at the same rate.

Can the tenants change their minds even after giving notice to not renew the rental contract?

Additionally, I got a rental appraisal certificate and it shows the rental is 13% more than the amount of current rental value.

So can I increase rent to the amount mentioned in the certificate or I can increase only 5%?