Several sources suggest lifting the lid (whatever it may be — some sources say to put plastic poked with holes, others are silent – I put paper towel over the jars) to stir the mixture once a day and let it sit for several days to a week. I did not stir mine but, rather, let it sit for longer than a week. I am pretty happy with how they turned out, especially the Oregon Springs, which all had plenty of water and not too much pulp/flesh. They separated very easily from the rest of the goo, which washed right off. Even though I’m having fun, it really is not the most pleasant experience. You have to not mind the smell of mold, and the sight of it. I’d like to feign the sensibilities of a more delicate being but, truth is, I’m just not. There’s almost something satisfying about the putrid pungence of the murky mixture that’s been lurking beneath the paper towel for weeks. I did stash them in the basement sink so as not to offend other members of the household. I may be masochistic but I’m far from sadistic. Anyway, thanks for joining this journey with me. It was my first time saving heirloom tomato seeds. If you want some, check out the info above on how to sign up for the Big BK Seed Etc. Exchange to take place Saturday, Sept. 17 I think … check above. I have some stinky tomato gunk I have to tend to…
The advice you found sounds more like sour dough starter. With starter, you stir it occasionally to distribute sugars and starches which are the food mold/ spores feed on. In a thick mixture like starter, mixing also releases trapped gasses which cause the volume to increase. The tomato mix doesn’t look too thick so expansion due to gas buildup may not be an issue. Sour dough starter is about as thick as pancake batter.
Depending on the type of starter you cover the jar to keep out stray organisms, and on some you periodically open the jar to let some in until things start fermenting. I would cover your jars, just not air tight in case gas pressure builds up too fast. The warmer your mixture the faster fermentation will go- up to a limit. With starter it’s best to keep it under 100 degrees or the organisms doing the fermentation will die.
While I know the above applies to sour dough starter, the process for fermenting tomato seeds should be pretty similar.