Hello there,
I'm sorry but this cannot work. As it says on the product page of the Level shifter:
"Works down to 1.8V on the low side, up to 10V on the high side"
so low side at teensy (3.3V) should do the job, but 12V on the HL side are just to much for this little chip.
Think it would be the easiest to buy 5V LED Strips or just use your 5V Power Supply. Are you sure the LEDs need 12V? If they work with 5V i would think they need 5V.... ;)
but would be best to have a look at the datasheet of your LED Strip!
In case you didn't know there's a special Adaptor for Teensy to drive up to 8 WS28 Strips. We don't have it in store right now, but you can get it from Adafruit: https://www.adafruit.com/products/1779
But it is also only for 5V LED Strips.
Maybe i'm not getting you right, you're saying it works with a 5V Power Supply connected to the LEDs and you bought the level shifter to connect your teensy to LEDs that work when they get 5V. Should be fine just don't use the 12V Power Supply.
Best Regards,
steffen