DaveGTR
It shouldn't. I watch alot of the Roku Channel LiveTV and either have them playing in different rooms at the same time, or more often, finish/continue watching a program in another room. I have both Roku devices and a RokuTV and have not seen the behavior you described.
It may be account related. The account may have one of your devices in another region erroneously.
See if this same behavior occurs on another free channel/app like PlutoTV or Tubi with their LiveTV. Maybe it is just isolated to the Roku Channel. If it across all the different LiveTV channels/apps, I think I would just Factory Reset all my devices and get a clean start.
If you do a little testing and see if confined to one or more of the channels/app, then could also help Roku Support narrow down issue as well.
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I also just tested with Duck Dynasty ch.639 Roku Channel and synced up fine between my Ultra and the RokuTV. (+/- half a second) but definitely playing same episode. (currently S2:E1) 10:30pm MT