When there is a large internal electric field of the crystal perpendicular to the k. It can be at a surface or in a bulk of complicated crystal. This mechanism can be seen in my paper:
If you put a normal electric field to effect of Rashba splitting in TI there will be no special effects, because the internal field has a much more value.
Article A Simplified Approach to the Problems of Room-Temperature Su...
The band inversion is necessary condition and nontrivial Chern number is sufficient condition. If RSOI does not break these two conditions it can exist in TI.