The checkmarks are used to track confirmations from trade partners. Since your trade partners likely work on jobs with other builders as well, when your trade partners receive a notification of a task assignment or a task summary, it will include a link for them to confirm that they are available and plan to be there on the dates requested.
When the trade partner confirms from the email notification, you will see the checkmark next to their name on the schedule indicating their response.
Since your team members are managed internally of where they should be when, they are not asked to confirm task assignments. As such, you will not see the checkmark next to their names on the schedule.