Any 401(k) plan that has a Designated Roth Account must also have a traditional account. It's impermissible to roll over a traditional account in one 401(k) plan to a Roth account in a 401(k) in a different plan. Rollovers from a traditional account in a 401(k) to a Roth account in a 401(k) are only permitted to be within a single 401(k) plan, called an In-plan Roth Rollover (IRR). No 401(k) plan is permitted to accept a rollover directly into their designated Roth account unless the distribution was from a designated Roth account in the other plan (and also cannot be a distribution from a Roth IRA).
It's not entirely clear what transaction was performed because what you've described is not permitted. If what you have described is what actually happened you need to contact your new employer's plan administrator immediately to make the necessary corrections.
It sounds like you received a check payable to you and you asked the new plan to deposit it into the designated Roth account in their plan which they should only have done if they believed that the distribution came from another designated Roth account. Also, if the distribution was paid to you, the old plan would have been required to withhold 20% for taxes, and unless you substituted other funds for the portion withheld for taxes that amount remains distributed and subject to tax and early-distribution penalty.
Hopefully you are still within the 60-day rollover window to be able to get corrected whatever needs to be corrected. The new plan might have to distribute the money deposited into the new plan as a failed rollover and then deposit the money into the traditional account in the plan as a proper rollover before the 60-day rollover period expires. You can then, plan permitting (not all plans do), do an IRR which is a taxable rollover from the traditional account to the Roth account.
