05 October 2017
TDS (under Sec 194C of Income Tax) is different & it is applicable. Since you are registered & service providor is unregistered, you have to pay GST under RCM (Sec 9(4)). You can take ITC of said GST paid under RCM & can set off against your final gst liability.
06 October 2017
As informed earlier, on your firm TDS is applicable under Income Tax. No TDS is attracted in GST on your firm. However single registration is sufficient for all purposes.