If the move of this IRA is being treated as a distribution, the custodian of the original account will issue Form 1099-R near the end of January. It's the new IRA's custodian who will report a rollover contribution on Form 5498. A custodian can issue a Form 5498 earlier, and often do if they have reason to believe that no new contributions will be made for the prior year, such as if you've already made a full-year's contribution to a different IRA account at the same custodian. However, a trustee-to-trustee transfer of an IRA to another of the same type is neither a distribution nor a rollover, so there should be no reporting on these forms at all for a proper trustee-to-trustee transfer of an IRA.
Many low-level employees don't understand the limitations on distributions and rollovers of IRAs, so they think that every movement of an IRA can be done by distribution and rollover and if they mistakenly report a distribution it's all good if reported as rolled over, when that's not necessarily the case. Non-spouse beneficiaries are IRAs are not permitted to do a distribution and rollover of an inherited IRA and there is a generally a limitation of one IRA-to-IRA distribution and rollover per 12-month period in other cases.
