KI 229 RMI and DME Stations
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Couple things to unpack here:
The question implies you are tuning a standalone DME. I am not sure where one would encounter such a thing, however DME as a system does not provide any bearing info. The RMI still requires actual bearing information from the VOR to set its pointer. It doesn't work like an ADF, where the needle just points towards the signal.
Regarding an ILS, the RMI should not point at the localizer. If you tune a localizer (IRL anyway), the RMI needle will park in its "off" position (pointing E-W). Localizers do not provide bearing information, only deviation. There is a "sim-ism" in MSFS where RMIs will point at localizers but this isn't accurate.