That's not exactly right.
From the splitter, run one leg of the cable into the cable box. Then run a set of cables (red/white/yellow, or red/white/s-video) from the cable box's output to the TiVo's input. Then run another set of cables from the TiVo's output to one of your TV's inputs.
Run the other leg of the split directly to your TV, to another input.
This will give you the abililty to TiVo the digital channels, and then when you want to watch something else while the TiVo records, you can just switch to the other input. On this input, you'll only get the analog channels. Unless you get another cable box for that leg. But if you do that, you'll probably need to build an IR fort for your TiVo to prevent IR interference.