We do not play this way officially. Any card, specifically those first edition Alpha and Razor that say “At any time” are used to signify “at any time during a turn but between the start and completion of phases”. Obviously, writing all of that on every card makes no sense so we used that “at any time” reference to mean between the phases. There are a couple cards that have between phase triggers but these cards will define that trigger specifically such as Darwin’s Objective in Edgehunter which may trigger during the middle of the Draw phase if a 10 or a negative value appears. The opponent can reveal and steal a card that you were about to move but this has to be done before you begin the new phase.

OFFICIAL: No, a card cannot interrupt in the middle of a Phase. Complete each phase and then perform the play on the card or trigger it before the phase is started.