Before — enrichment timing beats almost every other routing decision. If the router fires before firmographics land, it routes on a blank field and the rules you designed never execute. Enrich on entry, then route on the enriched record.
This is the single most common cause of "the routing is random" complaints from reps. The logic is usually correct; it is just evaluating nulls. Build an explicit wait-or-retry step between enrichment and assignment, and add a fallback queue for records enrichment genuinely can't resolve.
Every claim above comes from work LeanScale published. These are the sources.