Say, if the $T_t$ (time) dummy begins as $T_t=0$ then turns into $T_t=1$ when we have the treatment period and then goes again into $T_t=0$, how does the interpretation of the interaction term change ($D_iT_t$, when $D_i$ is the dummy for the units that received the treatment)?
In such situation, what would be (in general) the more adequate model in place of the DD?