I am looking for evidence that supports employee engagement as the mediator for well-being and performance. Is there any scale that has been developed to justify it?
Really, you should be using one measure for performance, and one for well-being. In order to test for the association between two variables, you will need two statistical artefacts (e.g. for the purpose of a correlation). The General Health Questionaire (GHQ) is quite a popular choice fo rmeasuring wellbeing, but I have used Warr's (1990) job-related affective wellbeing measure.
There are a range of methods for measuring self-reported job performance, but it may be worth considering whether it is possible for you to find a different approach to measuring job performance. People are not always accurate in their self-assessment of performance!