Well, I've found it. On some forum they said the plugin which supports the IntelliSense-like behavior is called Code Completion. In fact I've previously disabled that plugin, because I had no idea it could be linked to the info-displaying while hovering the cursor over an item (plus I didn't want to auto-complete my code).
I've enabled that plugin, so the checkbox with "Display info while hovering the cursor over a token" came white (able to select) so I've checked it. Then, I've disabled again the Code Completion plugin, but left the checkbox checked. Now it works perfectly.
Anyway, thanks for your help.
EDIT: Ah wait! Just one more thing.

Can I decrease in some way the time which I have to wait until the info is shown? It shows up after about 2.5 seconds and I want it to be shorter. I couldn't find it anywhere in the settings, help would be greatly appreciated.