You`ll need a payload hex for AT90USB-162 with an 8Mhz oscillator.You got a close copy to the teensy. The original Teensy got about 16Mhz, so that could be your problem i guess.
If you got it follow these steps carefully:
1. Launch Atmel Flip and select 'Device', Select the microcontroller that matches your board (In this case AT90USB162) and select OK.
2. Select 'File' - 'Load Hex File' - Select your .hex file
3. Select 'Settings' - 'Communication' - 'Open'
4. Click the 'Erase Target Device Memory button.
5. Click the 'Program Target Device Memory button.