"I am eating a tomato."
Pomidor (and many other food related words and/or plants) is exception to the "animation rule". It is "grammatically animated", which means it has accusative case=genitive case.
and you need accusative case after "jem".
So I chose pomidor and it said that it is correct and offered another version of translation with pomidora? What is correct now?
Both, actually. "Pomidor" is the "technically" correct version, but "pomidora" is so widely used that for the vast majority of natives it's the only option that sounds natural.
"Pomidor" is not technically animate, but it is usually treated as such and therefore most people say "pomidora".
Yes, I cannot imagine anyone saying "idę zapalić papieros", although that would theoretically be correct...