First, who is Carson Fulmer? He's a 5'11" 195 lb (some sources list him as 6'0", full disclosure) Right Handed Pitcher. He's a Starter at Vanderbilt University. His first year and a half at Vandy he was the team's Closer and transitioned to Starter a little over a year ago. He's a very max effort Pitcher, and it has worked for him, as his Fastball routinely sites 93-95 and he can get it up to 97 when he wants. He also has a 12-6 Curveball with a lot of snap to it. He also has a low-80's Changeup with very good movement.
We'll start with his Mechanics, because everything with a Pitcher starts there. They're violent. Like late 80's Agnostic Front Sunday matinee at CBGB's violent. Lot's of energy. His arm is incredibly fast, I can't even think of a comp for that violent an arm action. He has a few very troubling parts to this delivery that scream Reliever to me at full volume: 1. He throws across his body, which can lead to control problems and add stress to the elbow and 2. I've seen clips where he tends to lock his landing knee, this can cause pitches to end up higher in the zone than intended. As a shorter Pitcher already prone to flyballs because of the lack of downward plane on Pitches leaving things up would be very problematic as a pro.
Most of these issues are borne out in his results, as he has had control issues in both Relief and Starting roles. He has though been able to maintain his velocity late in starts and hasn't shown any injury issues to date. In the video below (courtesy of Jheremy Brown) you can see the max effort of his delivery. You can see a good example of his Curve at the 1:50 mark. You can also see the movement on his Fastball.
Now to talk Pitches, and we'll start with the Fastball, because everything that doesn't start with mechanics, starts with Fastballs. As mentioned above he reliably works low to mid 90's with good arm side run, though not much of any sink. It's a Plus Fastball all day. He can really give Righties trouble with it. As noted there are control issues and when he misses it tends to be inside to Right handed hitters.
His second best pitch is the power Curve. The Curve is also a Plus pitch with deep break and he has surprisingly good control of it (in context with his profile). He can drop it in for Strikes early in the count, then drop it in the dirt when looking for swings late in a count. It's a game changing Pitch at the College level, and I suspect that even against current MLB hitters he'd freeze some guys with it.
His third Pitch is an above average Changeup he throws in the upper-80's. It's a step below his other offerings and would rate Above-average. His flaws with it would only be that he does slow his arm when he's struggling with control of it. I think there's good potential with a few years of pro-coaching for this to top out as a fringe Plus pitch if they can tune his mechanics.
A lot about Fulmer screams Reliever to me: short, high effort delivery, control issues. What doesn't screm reliever is 3 potential Plus pitches. I want 200 innings of that guy, not a few innings here and there. You'll hear a ton of comps to former Vandy starter and current A's star Sonny Gray. Fulmer may actually have better raw pitches, but worse control and mechanics. So, here's a guy who could be a #1/2 Starter with a floor as a shutdown reliever. That makes him both a pretty safe and pretty risky pick. He may not make it to #10 though, as the Red Sox are reportedly very high on him.