Sample code demonstrating how to determine which complication family was tapped to launch your watchOS app

ComplicationLaunchSnippets.swift

// 1.
class ComplicationTimeKeeper{
    
    static let shared = ComplicationTimeKeeper()
   
    var utilitarianLarge : Date?
    var utilitarianSmall : Date?
    var circularSmall : Date?
    var modularLarge : Date?
    var modularSmall : Date?
}

// 2. in your CLKComplicationDataSource
func getCurrentTimelineEntry(for complication: CLKComplication, withHandler handler: @escaping ((CLKComplicationTimelineEntry?) -> Void)) { 
     
     // Call the handler with the current timeline entry
     switch complication.family {
     case .utilitarianLarge:
            
         let date = Date()
         ComplicationTimeKeeper.shared.utilitarianLarge = date
            
         let template = CLKComplicationTemplateUtilitarianLargeFlat()
         template.textProvider = CLKSimpleTextProvider(text:"Something")
            
         let timelineEntry = CLKComplicationTimelineEntry(date: date, complicationTemplate: template)
         handler(timelineEntry)
            
     default: handler(nil)
     }
}

// 3. in your WKExtensionDelegate
func handleUserActivity(_ userInfo: [AnyHashable : Any]?) {
    
    guard let userInfo = userInfo, let timelineDate = userInfo[CLKLaunchedTimelineEntryDateKey] as? Date else{
        return
    }
    
    if let utilLarge = ComplicationTimeKeeper.shared.utilitarianLarge, timelineDate.compare(utilLarge) == .orderedSame {
         WKExtension.shared().rootInterfaceController?.pushController(withName: "SomeController", context: nil)
    }
}