How to use cck time field in rules?
Below is a sample of a rule (in Rules export format) that will send an eMail similar to what is asked in the question:

{ "rules_notify_author_of_selected_field_updates" : {
    "LABEL" : "Notify author of selected field updates",
    "PLUGIN" : "reaction rule",
    "OWNER" : "rules",
    "REQUIRES" : [ "rules" ],
    "ON" : { "node_update" : [] },
    "IF" : [
      { "entity_has_field" : { "entity" : [ "node" ], "field" : "field_check_in" } },
      { "NOT data_is" : {
          "data" : [ "node-unchanged:field-check-in" ],
          "value" : [ "node:field-check-in" ]
        }
      }
    ],
    "DO" : [
      { "mail" : {
          "to" : "[site:current-user:mail]",
          "subject" : "Notification about a node with an update field_check_in value",
          "message" : "Go checkout the node with nid [node:nid] and title [node:title]: it has a field with an updated value (which is [node:field-check-in]) you wanted to be informed about ..."
        }
      }
    ]
  }
}


Some more details to further explain the above above sample:


The Rules event I'm using is "After updating existing content".
It's about updates to the field field_check_in.
The Rules Condition checks if the "The value changed".
If the Rules Condition is true, then (as Rules Action), an eMail will be triggered to the editing user.


Adapt the actual eMail details (subject, etc) to fit your needs. Then import it in your own site (using the Rules UI). That's it.

Note: I'm assuming this is about D7.