Rub Roast Before or After Searing?
I think there is a place for both. Without being aware of the particulars of this received wisdom/commandments from on high, it is a little hard to say. Seasoning of meat is often performed before searing (think steaks), but this is commonly only in the form of a thin layer of salt and pepper and maybe herbs too, not a thick complete covering. I have also seared roasts and then placed on a bed of herbs and garlic to roast - though not rubbed as such.

If you used seasoning as above and not a thick layer, then it would be reasonable to sear after rubbing. However, if you applied a thick layer so as to form a crust, these will have to heat up to searing temp before the meat could even approach a temperature at which the maillard reaction could occur. This would also be at or above the temperature at which the sugars in the herbs would also caramelize and start to burn, as happened in your case. In such a case I would not sear, unless in a very hot oven for maybe 5-10 min, before turning down to cooking temp.

It could also be that the family recipe only applies the rub to a portion of the meat, perhaps just the top/skin side, and only sears the bottom (or vice-versa I suppose).

Perhaps your girlfriend's family only use a thin layer of seasoning rub before searing.  It may be best to get an invite to her next family roast and ask to help in the kitchen while preparations are on-going. If you are looking long-term, incidentally this, and helping with the dishes, are a  way to get into the good books with her family too. Another option is to simply ask her how she does it!