There is a built in amplifier in all of the Tablo units to compensate (nothing “overcomes”) for the split. If it weren’t amplified, it would literally be a 50% degradation in the signal. If you look at any multi-tuner DVR (TiVo, Tablo, HDHomeRun, etc), they all have to have a splitter. If you get a single tuner DVR, it won’t have the splitter.
My experience is the Tablo seems to be venerable to errors in tuning, as it is transcoding the incoming signal, and needs to have a short buffer to compensate for the transcoding (it is a lot more technical that this). The TV can recover a bit more quickly/easily, but it doesn’t transcode the signal for streaming.
I experienced the errors with my TiVo (which I gave away to my brother). I was frustrated with the Tablo, but after much research I found that you can’t get the perfect device with an antenna.
I have two Tablo DVRs, two HDHomerun DVRs and multiple TVs in the house. All four of the DVRs experience similar issues. It happens with stations that sit on the digital cliff, but sometimes there is occasional interference from different sources (one of those is my water pik - I can’t clean my teeth when something is recording, or it errors out - and the TVs have the same issue).