Am I correct in my thinking that under the SCRA it is the responsibility of the servicemember to request the interest rate reduction and provide copies of orders and not the lenders responsibility to ask?

Yes. Section 527 of the SCRA.

http://www.bankersonline.com/regs/201/sscra.html#527

Because of the extended period the SM has to request this protection, if you believe they are eligible you can nudge them so they know what is needed, and if they want to request it. Doing this now may be easier than calculating the refund months or years later.