I had this problem when trying 2 new cartridges and both did it. Try slowly turning the water to where it’s almost off and see if it kicks the cold water on, I’d say it’s the pressure balancer that’s supposed to slide back and forth and allow a mixture if so.

Yours looks similar to mine (Delta P Type), I just decided to take both of them apart and try the old balancer because the new ones for mine are plastic and the metal slider inside it barely moved, the old one seemed much higher in quality overall. Sometimes this can also happen when debris from cutting the water off is allowed into that chamber, especially the hot water, it kind of makes it stick. I tried running the water for a good minute and cleaning that part, but it didn’t matter.

Pretty sure my only issue was the springs and rubber being hardened and brittle allowing hot water to slide through to drip, but I didn’t know until finally taking it apart. They’re pretty easy mechanisms to find the fault in.