Should it not be 'These people are big!? As 'Those' is 'Tamti'. Note: the person writing the comment is a native czech speaker now living in the UK not me.
Tito = these, Tamti = those. "Ti" as a demonstrative is not refering to a distance at all. But not having any context I'd choose "those".
I always hear Lidí, it's the first time I see Lidé! Can someone tell me the difference?
Lidi (not lidí) or Lidé, both are possible. There is no difference, there are simply two possible forms of the nominative plural.
Translation 'those are big people' is seen as incorrect but seems the same to me. A bug or is there really a difference?
The course routinely distinguishes between, for example, "That car is red" and "That is a red car." They are grammatically different sentences in both languages, and it is good to understand this early on. It will save you lots of head-scratching later. :-)