Time is not controlled by UCM. The router should be synchronized to the same NTP source as the UCM cluster.
Cisco IOS Network Management Configuration Guide, Release 12.4T - Configuring NTP
http://www.ciscosystems.com/en/US/docs/ios/netmgmt/configuration/guide/nm_basic_sys_manage_ps6441_TSD_Products_Configuration_Guide_Chapter.html#wp1001170
Example:
ntp source Loopback0
ntp master
ntp update-calendar
ntp server 198.82.1.201 source Loopback0
Also be sure to set the appropriate time zone and DST rules if applicable to your location.
Example:
clock timezone CST -6
clock summer-time CDT recurring
Lastly, the telephony-service or call-manager-fallback also has a time zone command that should be declared for the phones:
Example:
telephony-service
time-zone 8