If the definition of the present is that it a moment in which the future is not yet fixed or definite. Then travelling into the past would create a new present moment. It would dissolve the future you had left behind or the past would change as you interacted with it. So a universe with time travellers would have many present times and multiple different pasts. That is assuming the changes propagate as the time traveller experiences them.
If the definition of the present is that it a moment in which the future is not yet fixed or definite. Then travelling into the past would create a new present moment. It would dissolve the future you had left behind or the past would change as you interacted with it. So a universe with time travellers would have many present times and multiple different pasts. That is assuming the changes propagate as the time traveller experiences them.