The holder should clamp quill (round stationary part above the chuck) and be VERY secure. Since you are using a delta attachment on a rigid drill press it may not fit perfectly. Once you get that right, put whatever chisel in you are going to use as far as it will go. If there is a bushing/collar in it and it interferes, take it out. It may be for use with different size chisels. Then get your drill bit in. You need from 1/16" to 1/8" space between the chisel and the drill bit to allow chips to flow. If you don't do this, the drill bit will get hot and break. The bigger the chisel you use the more clearance you want for chip movement. I learned this the hard way with 4 drill bits, got mad, and went and bought a dedicated bench top mortiser and found out when I went back to Woodcraft in Kansas (I lived there at the time) and the guy working there explained it to me. Get your fence in position and then make sure you have your chisel square to the fence. Set your depth of cut, and then drill out each of the ends of your mortise first then work to the other side.
Make sure you have your hold down tight. Cutting large mortises can be a PITA as the chisel wants to stick and it puts a lot of torque on your press overall. Take your time, and it should work.