It’s designed to stay flexible for a long time. The metal points are what hold the glass into the frame, the putty is what keeps rain and wind from coming in around the glass. It couldn’t do it’s job if it hardened. It will, in a few days or so, form a skin that is paintable, but the body of the glazing will remain soft for several years. That’s how it’s suppose to work.
If you have already painted it you will just have to wait because the oil in the glazing putty and the oil in the primer will take a while to dry. Days? Weeks? It depends on the weather.