Yes. It sounds like he is the one who built the gun.
As for the 1861-1864 date, that is the time period that things like tax records and the like list him as a gunsmith.
He probably made guns before and after those dates but those dates can serve as a good indicator of when he was active.
As for needing to set the trigger before the gun can be cocked, this can be due to several things.
There is a style of set trigger that will only fire the gun by pulling the front trigger if the rear, set trigger is first set.
It usually needs to be set before the lock can be cocked.
This is known as a "single lever" double set trigger.
There is also a style of set trigger that can fire the gun by just pulling the front trigger without the rear trigger being set.
The front trigger pull with the set trigger in the unset condition usually takes a 2-5 pound force.
Setting the rear trigger first reduces the force needed on the front trigger to a few ounces.
This is called a "double lever", double set trigger.
(The "double set" refers to there being two separate triggers.)
If everything is right on a "double lever" trigger, the lock can be cocked without first setting the rear trigger.
If a double lever set trigger is installed too deeply into the stock, it can prevent the lock from being cocked to the full cock position.
This can usually be corrected by putting shims under the trigger plate.
To easily see if the trigger is a single lever or a double lever style, remove the lock from the stock.
Look down the hole in the wood that is there to provide clearance for the "sear arm" that sticks out away from the internal lock plate face.
While looking down this hole, pull the front trigger back as far as it will go.
If you see a metal "lever" rising upward and blocking off a good portion of the hole, the trigger is a double lever style.
If you don't see anything rising to block off the hole, the trigger is a single lever style.