Hm, you're a flute player who switched to drums with minimal experience and ended up on tenors?
That's peculiar, because tenor players certainly should be fluent percussionists.
In any case, I have some tips.
First of all: Call them what you want, srsly. My band has 5 drum-tenors. We call them quads, quints, and tenors. They're called quads because they have 4 drums that are tuned to each other, and 0-2 drums that are pitched as high as possible (usually) simply for effect. Quads, quints, tenors, whatever. Means the same thing.
Tips:
Don't rely on melodies around the drums to memorize exercises. Learn them on one drum. In fact, before playing an exercise on multiple drums, you should hack it out on one drum.
My biggest pet peeve for tenor players is not playing in their zones. I've seen tenor lines that take no note for their zones. KNOW THEM.

Those are your zones. It's really easy to forget about them, but if you play within the zones, your drums sound the best. They're pretty much just mini timpani.
Know your rudiments, like the person above said. Paradiddles, double paradiddles, paradiddlediddles, hereta exercises. You will need them for tenors.
Work on your diddles like crazy. Yes, the sustain that you get from tenors can mask faulty diddles, but if you want to pursue tenors, get your diddles open. Ridiculously open. Get them to be even, because when you get to more complicated tenor technique (getting to sweeps/scrapes, crossovers, and the like) If you have your diddles set, you'll have no trouble picking up more advanced techniques.
Again, like the other person above, practice. You need to practice to hope to sound good at all.