All limbs aren't made the same, even by the same manufacturer. Your newer limbs could be a tad shorter. For example, the nocks might be cut an eight or a quarter inch shorter. So if you put your old string on the new limbs, it would be too long, and a low brace height would result.
And, as already noted, a low brace height can lead to the string slapping your wrist. Or, maybe as you said, the string just untwisted a bit in changing from one set of limbs to another. Regardless, the problem does seem to be a low brace height so just need to raise it. Good luck.