I do not have the manual handy right now, but I think just one solenoid would cause that, but not sure off the top of my head which one it is, but yes. You can try cutting the power to the ECU by pulling the fuse (under the passenger side dash near the TCU computer) and starting up in 1-2, then shift to 3, then down shift to 1-2 at about 15-20 mph to see if it downshifts to 2 instead of 1 and stays in 2 to confirm it is not clutch plates or bands going bad or hydraulics....
Good chance it is a solenoid. They can be tested with an ohm meter, need to read about 8 ohms across the 2 wires.