The disability contracts should be written as "contributory", meaning the employees are paying some or all of the cost of coverage. The carriers typically rate up, even if 100% participation is required. How the employer charges the employee for coverage (pre or post-tax payroll deduction, or gross up then post-tax deduction, or adding imputed income to taxable income) is typically up to the employer and not in the carrier plan documents.
You can check the master policy and the certificate for that language (should state who is paying for the coverage in the ERISA section). The carrier should verify if 100% participation is required, which is typical even if written as "contributory". The carriers are familiar with employees paying taxes on the premium in order to have tax-free benefits (and the IRS agrees this is the same as paying for coverage). When there is a claim, the claim form then indicates that the employee paid for the coverage (so that the carrier knows the benefits are tax-free).
The company should consult with its tax advisor on any W-2 corrections to the premiums that were taxed. The broker needs to fix the contract (have written and rated as "contributory") if the company wants employees to have tax-free benefits going forward. Or, the company could leave the contract alone, pay the premium, and any disability benefits are taxable - when employers have difficulty administering a plan properly, sometimes it is best to keep it simple.
Hope this helps.