One, Not Both

The Atlas slide switches will work with twin-coil solenoid type machines as these require a momentary contact type controller.  The NJ switch machines that I'm familiar with are this type of device.

The Tortoise on the other hand, requires a constant contact control as it is a motor.  It draws current constantly and simply stalls at the end of it's throw, the motor continually appling pressure to keep the points snug to the stock rails.  It will require a SPDT toggle or slide switch.

An alternative

If the Atlas slide switch is used to control a magnetic latching relay, then the Tortoise could be used - the relay applying the correct polarity continuously to the Tortoise motor. This is only true for latching relays that use magnetic latching method. Magnetic latching (most) relays are dual coil. The NJ dual coil switch machines usually include DPDT contacts, which would serve as a latching relay - the NJ switch machine would not be linked to the turnout, but serve as a relay.