Sometimes you have a loose fitting washer on the center diverter.
If that is missing, it will only divert some water.
I have a 3-handle tub/shower that was leaking. I decided to replace the hardware for all 3 valves while I was at it. Luckily there was a kit available that included new seats, stems, handles, the whole nine yards. Everything went smoothly and the leak is now resolved. However, now when I turn the diverter handle to the shower position, only about 50% of the water is diverted. The rest of the flow continues from the tub spout. I've had this problem once years ago, but I can't recall what the fix was. I am baffled since everything from the seats outward is brand new.
Typically, the diverter stem has a rubber washer at the hose ( this keeps water out of the shower when using tub) AND another gasket, often hard nylon, behind the nose. This stops water from going to the tub during shower. That washer may be missing, damaged at install, OR pieces of the original one may have broken off, and were unnoticed, and are still floating around the body. Remove the diverter stem and have a good looksee with a flashlight ....post some pics.
If the valve is like the one in Terry's picture and the old fiber washer (950-060) stuck inside when you took it apart, there are now two washers stacked up there. This won't let the diverter washer (950-040) bottom out and seal against the body of the valve. Try removing that fibre.