I suggest delinking the appraisal date from the anniversary date. Instead, have a cutoff date.
For example, say that they will need to be in the system for X days/weeks before they are eligible for appraisal.
If you decide on say 45 working days, you can then see who is eligible when and offer them pay hikes or bonuses on a pro-rated basis
For ineligible people, you can have a policy where they can be eligible for a discretionary bonus if they perform extraordinarily well.