First time in a drysuit

I bought a used baggy-style drysuit off e-bay and it arrived yesterday. So off to Lake Mead I go today. Water was 67 degrees and pure glass over the entire Overton Arm, BTW. I wish it were like this all summer. Air temp was 75 degrees and not a bit of wind. So I put on the drysuit, wearing only my regular swimtrunks underneath. By the time I got the thing completely done up and board on, I was pretty warm. I think I was sweating a little bit before I hit the water. I felt like the seals were tight, and I even had to pull on the neck a little to release some air after I put on my life jacket. After my run, I unzipped and I felt like I was wet. Sure enough, my chest and legs looked wet but my swimsuit felt dry. Is this normal if you don't wear a shirt under a drysuit? Do you guys usually wear some type of long-johns underneath?