Add spice then oil, or oil then spice?

Well, this is rather complex. Let me break it down in two parts:

1. Oil on the meat vs. oil in the pan
   There are two advantages to oiling your meat instead of pouring oil in the pan: Less splattering and typically less oil used overall.
   But keep in mind which oils you use: For frying / searing you want something with a high smoke point. Leave your extra virgin for cold or only slightly warm uses.
2. Oil or spices first
   Your meat should be dry before you put it in the hot pan or you will end up with possibly painful splatters, or at least a lot of extra cleanup (see 1.). So you should always dry your meat, e.g. with paper towels. This will mean your spices are less likely to stick to the surface. Oiling the meat first helps the spices to adhere better, rubbing them in or just sprinkling doesn't make much of a difference.

One important element is to differentiate salt from other spices. Salt (and to a much lesser extent sugar) will do two things that other spices won't: (1) it will penetrate more deeply into the meat, and (2) it will cause the surface to moisten temporarily before that moisture is reabsorbed.

If you want salt to penetrate the meat, you should apply it well in advance and without oil. Oil will make it take longer for the salt to be absorbed (and thus it may not penetrate as deeply). And salting in advance (preferably at least an hour ahead of time) will allow the surface moisture to be reabsorbed before cooking, avoiding splatter and "steaming" effects that will inhibit browning and flavor reactions.

For the remainder of the spices/herbs, timing and order doesn't matter as much; larger flavor molecules won't penetrate very deeply. Usually oil is used to help them stick, which mostly happens by moistening the spices/herbs. So it doesn't really matter much whether you put the spices or oil first, or whether you mix them together and make a paste that you then apply to the meat. (Some people use mustard, some other sauce, or even water to help the spices adhere.) The main time it can make a little difference is if you have spices in a fine powdered form that will clump together when mixed with oil. In this case, it often makes sense to rub them on the dry meat first to spread them evenly. Conversely, very large pieces of herbs or whole seeds/peppercorns may not adhere well to dry meat, so moistening the surface first could have an advantage.

Since your goal is to keep the spices on, rubbing will be more effective than sprinkling, again particularly with fine or powdered spices. The surface of meat is generally full of small uneven areas, and rubbing can push those spices into any small fissures or holes (where they're less likely to fall off). This is less important with larger pieces of herbs, whole seeds/peppercorns, etc., but you'll generally expect a lot of those to fall off during cooking anyway.

As for oiling the meat vs. oil in the pan, the main advantage to oiling the meat is when applying spices to create better adhesion. If you're not putting on spices, you don't need the "adhesive" oil on the meat. Some claim that you'll get a better crust when searing by oiling the meat, though if that's your goal, getting a better crust is even easier by using more oil in the pan. I'd also say that whether you'll use less oil or not depends on whether you're using a non-stick pan. For a standard stainless pan (or other pan that is NOT non-stick), some oil in the pan is going to be necessary to prevent sticking anyway. And in that case, oil in the pan is going to help any spices/herbs from sticking too (and coming off the meat), more so than the oil on the meat.

Another take on this: this method works well for Indian curries, where you may have larger spices like clove, cardamom, peppercorns, that you don't want to end up in the dish. Heat the spices in a pan to release the volatile aromatics, then add oil to spread the flavor, remove the larger spices and then cook the vegetables, meat. etc.