How is that you issued appointment letter but not issued it? Your first sentence contradicts the second wherein you had mentioned that in the letter it is mentioned as 'probation period'. However being in probationary period is no bar for ESI nor for PF inclusion. Only apprentice are exempted for ESI but not trainees/probationers. If any affected employee takes up the issue with the local labour office it will definitely create unwanted issues for your company. It is better that you try to convince your management to adhere to the rules and regulations. Prepare notes and send it over to your management stating the rules as it is and the sections related. You try to do your part in convincing them to act immediate.
Thanks and Regards
22nd January 2019 From India, Hyderabad