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if both capture the same object, a check is performed (to see if only one player entered the object). If both players are involved, the system interrupts the turns, giving the opportunity to replay the turn without Overmind for red (with changes made by blue), then a turn without Overmind for blue;
after this, the game continues with Overmind;

(our time spent is a higher priority than minor nuances with scouting I proceed from this principle)

if blue attacked red on the previous day, it interrupts and rolls back his current turn; red re-plays his turn that he was playing; and blue continues his turn at this moment, but he still sees red's heroes as they were on the previous day (roughly speaking, red becomes blue, and blue becomes red in terms of turn priority), and if at this moment red attacks another of blue's heroes, blue's turn is rolled back, and he re-plays his current turn with the changes inflicted by red, but red retains the changes inflicted by blue