In addition to adhering to the policies and guidelines of

Let us edit the text a little to make it clearer.

In addition to adhering to the policies and guidelines of the State Department of Education, the successful instructor will (be responsible for instruction in the appropriate teaching environment and (will) evaluate student learning.) The important thing to remember here is that the – will - in the second part is elliptical, unmentioned but understood.

The instructor will have to do two things, because these are duties that are associated with his actual work in the future. . So a future tense is required and present tense is inappropriate.

In A –evaluates - does not gel with the -will - of the first part
B - will be responsible and (will) evaluate is the correct expression
C -(The instructor) is responsible …. and the instructor evaluate – miss both parallelism and SV agreement

D - Is being responsible is an untouchable expression in the GMAT domain
E - present tense in the first part and will be evaluating in the second part are unsymmetrical

So B is the best bet.