Circle is all about tracking and filtering content that comes from the Internet, like any online application that downloads data.
However, Circle cannot track or filter cellular functionality, like a phone call over the cellular network or sending/receiving SMS-based text messages. These services are transmitted through your cellular carrier and, in the vast majority of cases, aren't traveling over the Internet and thus are invisible to Circle. In addition, because of how Apple handles their services, Circle is currently unable to fully manage or stop iMessages from sending or being delivered.
Some messaging-based services (in addition to iMessage) are not manageable by Circle. With these the source of the message in both directions is not tied to a particular server or domain name. This makes it impossible to track the platform it originated from. In these cases, when Circle has paused the entire Internet for a profile or device (including during an OffTime/BedTime) only sending messages will be blocked. You can read more about how iMessage works with Circle here.
Because Circle only monitors outgoing traffic, some services, especially those that utilize push notifications, may still be able to send previews of incoming texts or emails. Attempting to download the full content, or reply to the received message, will not work however. Circle cannot guarantee that these services will always be unavailable.