Teferi's last ability means that in order for an opponent to cast a spell, it must be that opponent's turn, during a main phase, and the stack must be empty. This is true even if a rule or effect allows a sorcery to be cast at another time.

If an effect allows an opponent to cast spells any time they could cast an instant (for example, if your opponent also controls Teferi), the restriction of Teferi's last ability takes precedence over that permission.

If a spell on the stack has split second while you control Teferi, you can't suspend creature cards since split second stops you from casting them, even though suspending them is a special action.

While you control Teferi, you may exile creature cards in your hand with suspend any time you could cast an instant.

If a spell or ability lets an opponent cast a spell as part of its effect (such as suspend and rebound do), that opponent can't cast that spell since the resolving ability is still on the stack. This is true even if the spell is an instant.