The Apple Time Machine program is not installed on the My Cloud. The Time Machine program is installed on the Macintosh computer. What the My Cloud does is support being a backup target for the Time Machine program on the Macintosh computer. The My Cloud is, at it’s core, a network attached storage device (NAS).
Currently WD states the following with respect to Time Machine: “… and the My Cloud drive is compatible with Apple Time Machine for Mac users.”
Like any other hard drive the internal hard drive within the My Cloud can (and sometimes does) fail. It is why WD includes the Safepoint / Backup feature within the My Cloud Dashboard so users, if they choose to enable/configure that option, can have a backup of their My Cloud data (typically to a USB hard drive attached to the My Cloud USB port).
If one has mission critical data, using a multi bay My Cloud or similar NAS with RAID support is typically the better option as they offer data redundancy (depending how the RAID is configured) than the single bay NAS drives do.
If one needs information on how to shut down a My Cloud device, WD has a Support Knowledgebase article covering the official way(s) of shutting the device down.