To make the dumpling filling stick to the wrapper, it has to be sticky. That’s really the main reason why the meat is minced and a little flour or starch is optionally added as a binder. If the filling is wet (i.e., watery) rather than sticky, as is the case with already cooked meat, the filling will pull away from the wrapper during steaming or frying. There are, of course, exceptions to the rule.
When the meat is gelatinous, it is possible to mince it after cooking and use it as dumpling filling.
This, we were first able to prove to ourselves a decade ago when my husband, Speedy, wanted to make fried wonton using cooked beef tripe. Oh, and this is the part where I say that Speedy made the dumplings, pleating and all. He does the pleating better than I do. Seriously.
Speedy started with cooked tripe that had been chilled overnight in the fridge. He minced it, added chopped vegetables, stuffed the mixture into the wrappers and fried the dumplings. Perfectly executed but the filling turned out bland.

So, he made a second batch. There was about a cup of leftover spicy tofu and shiitake mushrooms with miso sauce from our lunch. He minced the leftover, stirred in the minced tripe, used the mixture as dumpling filling and… success!!!
Later… much, much later, I realized that using cooked filling for making fried spring rolls is just as true.
Check out the following spring roll recipes where the filling is fully cooked before they were wrapped and rolled with spring roll wrappers.