The Mailchimp class provided by mailchimp (required for mailchimp integration) seems to not work on some servers. Not sure what the root cause is... I sent an inquiry to Mailchimp but haven't heard back from them.
The plugin doesn't have a timer itself it just gets the system time (meaning it just gets the server's time). It's kind of like if you run an application in your PC it doesn't have a timer itself... it will just get the time from the system so if your timezone in the PC is not set correctly the time in the application will be wrong too.