Tenor sax is concert pitch Bb, which is a full step down from C. Could explain some confusion.
As for pitch memory, I'm not real good at it, but when I write, I cross sences in an attempt to "describe" the overall feel of a key in order to choose appropriately for what I want to convey to the listener. For instance, a piece written in Cmaj would be described as "<fat> blue (the actual color, not the emotion/mood)." A piece written in Dmaj would be described as "royal, triumphant." Bb is "dark, sad."
These are some of my associations given as possible help.
One thing I would warn against is, as you continue in your singing career, DO NOT use memory of muscle tension or lip/mouth formation as pitch association, as you can be sharp or flat depending on mood, time of day, etc. True pitch association/recall for me, at least, is an actual form in my memory. Can't describe it, but it's real nonetheless.
My buddy Mahesh is giving good advice as well. Most guitar tuners have built in microphones. You could tune your sax (remember to compensate for concert pitch) as well as use it for voice.
Otherwise, practice, and if you can afford it, some good professional instruction will go far.
Cho