Well, two things are happening. Your hammer and sear engagement may be fine, but your grip safety is not blocking the trigger when you pull it back. There is a 'nose' that projects forward and is supposed to block the trigger from moving far enough to trip the sear until you depress the grip safety, then that part swings up out of the way of the trigger. If the nose is too short, it does not block the trigger and the hammer falls. Also the nose part may have been 'thinned' top to bottom. (I have done this before so the grip safety would disengage sooner) If that is done to much then the trigger can nudge past it and depress it as you pull the trigger and the hammer falls. You need to start with a new grip safety and properly fit it. If your hammer will fall when the trigger is pulled with the gun 'cocked and locked' then the thumb safety is defective also. When properly fitted, the thumb safety does not allow the sear to move so the hammer cannot drop. Again, a new one will have to be fitted as you need more material on the bottom 'V' inside the gun. This is not a big deal if you have a little experience, but if you question it at all, take it to a gunsmith. You do have an unsafe gun.
Sometimes you can drop parts in and they will work fine, but sometimes not. Since essex sell frames, this is probably a 'parts' gun. Obviously the parts you have are not working together properly. Sometimes the frame itself may be out of spec, and the holes for the pins misplaced slightly. This is usually correctable with the right combination of parts, but 'drop in's probably won't do it. I once built a gun up with an older Colt slide like you have and an AMT stainless frame. The magazine release hole was too low for that combination and I had to have a welder add a little material to the 'shelf' on the magazine release to raise the magazine slightly in the frame. Sometimes you get lucky and I do think that frames now are much more precision that they have ever been, but usually a 'parts gun' is a lot of work and fitting to get everything to work as it should. 44 Man