Yes, you should definitely use a spray-on.
Arcteryx themselves explicitly state not to use wash-in (product care information) and Gore-Tex does it implicitly by telling you to apply "to the garments outer fabric" (washing instructions).
You already stated the reason for this: DWRs function is to keep away the moisture from the "functional" layer to provide better circumstances for moisture getting from the inside to the outside. From the inside it is the opposite: We want the moisture to reach this layer, so there should not be DWR.
The following is pure speculation: I guess the makers of wash-in DWR are aware of this and probably designed their product to only or at least mainly adhere to the material of the outside of a garment. However especially the inside material can vary considerably by manufacturer and model, so even if the above is true it is hardly possible to make the wash-in target specific for all these material types.