Next run time for cloudwatch rate expression

It counts from the date and time you created the CloudWatch event. If your rate expression is rate(1 day) and you created the event at 22:00:00 UTC, then it will run at that time the next day. A rate expression for 2 days will fire two days later at the same time. And similarly a rate expression at 5 minutes will fire every five minutes beginning at the time the CloudWatch event was created.

To verify this, you can create a Lambda function that uploads an object to an S3 bucket, create a CloudWatch event for it, making note of the time you created it, and observe that when the event fires, the modification date of the object is that many days/minutes/hours from the time you created the event.