I don't use this API so my answer will be based your code and Spotify's reference documentation.

I think there are a few things wrong with your flow:

1. As Robert Dresler commented, you should (approximately) never call a delegate directly, a delegate calls you.
2. I'm pretty sure your action currently results in jumping to exactly 10 seconds, not by 10 seconds.

(As an aside, I'd suggest changing the name of your function moveFrdBtnAction to at least add more vowels)

Anyway, here's my best guess at what you want:

// forward button action 
@IBAction func moveForwardButtonAction(_ sender: Any) {
   skipAudio(by: 10)
}

@IBAction func moveBackButtonAction(_ sender: Any) {
   skipAudio(by: -10)
}

func skipAudio(by interval: TimeInterval) {
   if let player = player {
      let position = player.playbackState.position // The documentation alludes to milliseconds but examples don't.
         player.seek(to: position + interval, callback: { (error) in
         // Handle the error (if any)
      })
   }
}

// spotify delegate method seekToPosition
func audioStreaming(_ audioStreaming: SPTAudioStreamingController!, didSeekToPosition position: TimeInterval) {
   // Update your UI
}

Note that I have not handled seeking before the start of the track, nor after the end which could happen with a simple position + interval. The API may handle this for you, or not.

You could take a look at the examples here: spotify/ios-sdk. In the NowPlayingView example they use the 'seekForward15Seconds', maybe you could use that? If you still need 10s I have added a function below. The position is in milliseconds.

"position: The position to seek to in milliseconds" docs

ViewController.swift

var appRemote: SPTAppRemote {
    get {
        return AppDelegate.sharedInstance.appRemote
    }
}

fileprivate func seekForward15Seconds() {
    appRemote.playerAPI?.seekForward15Seconds(defaultCallback)
}

fileprivate seekBackward15Seconds() {
    appRemote.playerAPI?.seekBackward15Seconds(defaultCallback)
}

// TODO: Or you could try this function
func seekForward(seconds: Int){
    appRemote.playerAPI?.getPlayerState({ (result, error) in
        // playback position in milliseconds
        let current_position = self.playerState?.playbackPosition
        let seconds_in_milliseconds = seconds * 1000

        self.appRemote.playerAPI?.seek(toPosition: current_position + seconds_in_milliseconds, callback: { (result, error) in
            guard error == nil else {
                print(error)
                return
            }
        })
    })
}

var defaultCallback: SPTAppRemoteCallback {
        get {
            return {[weak self] _, error in
                if let error = error {
                    self?.displayError(error as NSError)
                }
            }
        }
    }

AppDelegate.swift

lazy var appRemote: SPTAppRemote = {
        let configuration = SPTConfiguration(clientID: self.clientIdentifier, redirectURL: self.redirectUri)
        let appRemote = SPTAppRemote(configuration: configuration, logLevel: .debug)
        appRemote.connectionParameters.accessToken = self.accessToken
        appRemote.delegate = self
        return appRemote
    }()

    class var sharedInstance: AppDelegate {
        get {
            return UIApplication.shared.delegate as! AppDelegate
        }
    }

Edit1:

For this to work you need to follow the Prepare Your Environment:

Add the SpotifyiOS.framework to your Xcode project

Hope it helps!