The rules say:
REGIMENTAL DOCTRINES
If your army is Battle-forged, all <TEMPESTUS REGIMENT> units in a MILITARUM TEMPESTUS Detachment gain a Regimental Doctrine selected from those presented below, so long as every unit in that Detachment (excluding the Advisors and Auxilla mentioned below) has the same <TEMPESTUS REGIMENT> keyword.
So for Matched Play we have the standard wording that every unit in your
army detachment needs to hail from the same sub-faction in order to get your special bonus.
For Crusade you get this additional text:
CRUSADE
If all of the MILITARUM TEMPESTUS units in a Detachment are from the same Tempestus Regiment, it gains access to the Regimental Doctrines, Warlord Traits, Heirlooms of the Regiments and Stratagems rules, as outlined below.
This would mean you can mix MILITARUM TEMPESTUS units with your regular regimental units in a single detachment and both parts of your army get their respective bonus.
Opinions?