I think it is a known problem, probably long standing, and Tablo is working on it; but the fix will be in a release with many Chromecast improvements, so it will be awhile.
I believe this or similar problems with Tablo Live have been reported many times. Here is a topic in the Support category that includes recent discussion of the upcoming fix. The chatter also includes the usual about switching to Roku, but I have dozens of other uses for Chromecast, and given Chromecast Ultra have no need to switch. I also like the Chromecast strategy, including using my phone or tablet as the focal point for all TV, music, film, … content.
Live TV starts at beginning of show every time when using Chromecast
This kind of thing is very frustrating. It’s good that we now have Tablo Ultra to deal with some of the other problems.
I don’t use Tablo Live. I only use Tablo for recordings. When I first got the Tablo in 2015, I found a lot of problems with Live. But I haven’t tried it in over a year, so am far from current.
For other reasons, I decided to have one antenna for Tablo and one for each TV. For live viewing, input straight from antenna to TV provides better quality for 1080i and 480i; and people can use the TV remotes rather than learn Tablo. This might seem like a workaround, but even if Tablo Live functioned perfectly, I think I would stay with my current scheme, using antenna for live viewing.
During my initial testing, I tried to find workarounds for Tablo Live problems, but that experience is far outdated. I have been meaning to try Tablo Live with Chromecast Ultra, just out of curiosity, and If I do will report under some appropriate Support topic.
In any case, one of the reasons I got my first HD TV was for 1080i soccer, so I’m sticking with antenna for live viewing.
One other concern about defaulting to the “live” time period. This might not be what the Tablo redesign team has on mind, although I think that best suits most users. Just a warning that you might not get exactly what you want in the upcoming release.