For a tubeless setup you need three things: the right rim, the right tire, the right valve-stem. Carbon side up shows how to identify the valve stem, and the tire and rim should be marked, but you need to check all three, because having tires and rims rated for tubeless may be used with a tube (I do this all the time on riding lawn mowers because their rims suck and leak even though designed for tubeless operation.)
However in your case there is an easy check since there is a flat tire. First look at the valve stem. If it is a presta use your fingers to loosen the stem nut (skip if it is too tight to loosen by hand), then wiggle the tire relative to the rim while watching the valve stem. if wiggling the tire moves the valve stem you have a tube if you feel the tube stretching against the valve stem, you have a tube, otherwise either you have a tubeless setup or a burst tube.