Why Heimerdinger's turrets don't apply the Liandry's Torment debuff but Zyra's plants does. I mean, i can understand if it's a nerf, but I just want to know how the logic of the game works

Placing a turret is a spell, which causes a minion to sit around until killed. Plants are an interaction between two spells, and have very limited life spans.

To elaborate, Zyra seems to be a special case where Thornspitters proc as spell casts (i.e. they proc spellvamp, Rylai's, etc.) I'm not sure this should be the case, as Heim has to spend an ultimate to get his turrets to slow, but it seems to be the case nonetheless. The logic behind this, as far as I can see, is that the base spell (Deadly Bloom - Q) procs these effects by itself. Seeds don't deal damage (by themselves) as far as I know, and therefore it's moot to discuss Rylai's and spellvamp (and thus Liandry's) with them. I wish I could give a better answer here, but I think you're right that there's a disconnect here. Even though the base spell procs, Zyra's plants should be treated like heim's turrets; any special abilities they have should be inherent, or boosted solely by Zyra's abilities, unless item procs are going to be treated universally across turrets and/or pets.