Yes! DNS Notify is a revision to the DNS standard (RFC 1996) that proposes that the master server for a zone notify certain secondary servers in that zone of changes, and the secondary servers can then check to see whether they need to initiate a zone transfer. This process can help improve consistency of zone data among secondary servers.
Total Uptime does support this feature. If you have configured secondary DNS on another server or another provider, we will send a NOTIFY message to the secondary servers that are specified as NS records within your domain. If you do not specify them as NS records, they will not receive the message. If you want to NOTIFY a server that is not listed as an NS record (e.g. a hidden server), then you need to use our ALSO NOTIFY feature. This can be set from the main DOMAINS tab by clicking your domain to highlight it in blue, and then clicking EDIT from the tool bar. This will open a dialog where you can specify IP address(es), one per line, for the server(s) that you would like us to also notify.
See the image below for the location of the edit button and how to enter IP address(es) into the dialog box.