i qualified on the USS Truman in May ... there are specific rules you must follow (at least for the Truman for this particular bounce period) ...
for departing the patttern on the Cat shot or a "bolter": once airborne & two positive indications of climb, you raised your gear and flew at 500 feet on the ships course heading at 300 knots till 7 DME from the boat ... then you climbed to whatever departure altitude that was given (for us it was 10000' MSL) and turn towards the "pigeons" heading we were given before the Cat shot.
if you were launching into the Landing Pattern: same deal, 2 pos rates climb then raise gear ... but climb to pattern altitude of 600' AGL and find your interval to turn downwind.
carrier quals for students are done Solo but there are many IP's in, around, and above the pattern keeping a watchful eye on the "studs", as well as the watchful eye of the "Air Boss" and "mini Boss" in the tower.
semper fi