We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for LDM, TSTIT and XSTIT. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3LDM and G3TSTIT are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also XSTIT can be characterized through relational frames, omitting the use of BT+AC frames.