During communications between the UT and an upstream device, do I have to set the Remote/Local operation mode to Remote?

Communication itself is available in either Remote or Local mode.
Switching to Remote mode is for overwriting r.SP from an external device.

Advanced Application UT75A

The UT75A temperature controllers employ an easy-to-read, 14-segment large color LCD display, along with navigation keys, thus greatly increasing the monitoring and operating capabilities. A ladder sequence function is included as standard. The short depth of the controller helps save instrument panel space. The UT75A also support open networks such as Ethernet communication.
Mid-level UT55A/UT52A

The UT55A and UT52A temperature controllers employ an easy-to-read, 14-segment large color LCD display, along with navigation keys, thus greatly increasing the monitoring and operating capabilities. A ladder sequence function is included as standard. The short depth of the controller helps save instrument panel space. The UT55A/UT52A also support open networks such as Ethernet communication.
UT35A/UT32A

The UT35A and UT32A temperature controllers employ an easy-to-read, 14-segment large color LCD display, along with navigation keys, thus greatly increasing the monitoring and operating capabilities. A ladder sequence function is included as standard. The short depth of the controller helps save instrument panel space. The UT35A/UT32A also support open networks such as Ethernet communication.