so basically just run them at 5v instead of 12v?
My earlier post was only focused on BobA's comment on the 5v device "not matching" the 12v LEDs, not about your specific wiring configuration.
Reviewed your original post closer and noticed that you were powering the LEDs with 12v from your computer power supply, connected through the buttons to the ground on your 5v encoder.
Question 1 - Can 12v LED buttons light up with only 5v? - Definitely yes, though not quite as bright.
Question 2 - Can using the power supply for 5v and the encoder for ground cause damage to the encoder? -

You might want to ask Bryan about that. Your picture showed 5 lit buttons. Assuming that each is drawing 20 mA, that gives you 100mA flowing through the encoder ground. Personally, I'd rather not risk it unless I knew for sure it would be fine. --Who knows, I might have to reorder and wait for Susan to ship it.

I Keed. I Keed. Luv ya Susan.--
Question 3 - Is your heart absolutely set on the LEDs turning off when you press the buttons? - If you don't mind them constant on, wire them with either 12v or 5v and ground from your computer power supply.
Wish I could give you a definite answer on Q2. Maybe someone who is using a similar setup can throw their 2 cents in.
Scott
P.S. Are you just lighting your 5 admin buttons, or will you be lighting other buttons as well?