"Any thoughts?" Never ask me that unless you have a lot of time to listen (and don't mind if the thoughts are not necessarily on target).
Part of the key is the contract you have with the employer. Read it carefully, and don't sign unless you like it. You're the professional, and your patients/clients are entitled to have you stick up for what's right more than for your paycheck. The employer is a "third-" (not second-) party payer. If your contract says you are an agent of the employer (for example, with respect to telling them things that might affect job performance or company assets), you should (and proably must) disclose that to the client before you start treatment. That's not the best of situations, but it is not unique (cf., therapists in the military or in prisons).
Otherwise, your duty is not to the person who pays you, but to your patient (that's why I use the term "patient"; it crystallizes the fact that you have a legal duty (even though I am NOT giving legal advice) to act in your patient's interest at all times. Very few things modify that duty (e.g., imminent, serious danger to others in most communities); who pays the bill is not one of them nor is your impulse to cooperate with a supervisor who calls you asking for follow-up.
In my experience (but let's hear from some EAP therapists and counselors out there!), once you disclose your relationship with the employer, and assuming you are not required to report non-dangerous things, patients usually settle in and work. If the issue is more serious, then it may not be something an EAP should handle, and referral is in order.
Note that it is VERY important that you know who is or is not entitled to information about the client, even if there is some kind of general release to communicate with the employer. There is some interesting new caselaw on this in California, and each state is different; however, I suggest that you never communicate with coworkers or supervisors without explicit permission. When some form of contact or report is required, a senior human resources person or company attorney is a much better choice.
The bottom line: have a clear agreement beforehand, and make it available to your patients/clients.