Switch State Issues?

Maybe by adding comments into your code you could see the faulty logic flow.

Or perhaps missing / misplaced code lines?
Or wrong time checks?

CAPITALS USED FOR EMPHASIS

//set correct pin numbers as required
#define reedswitch 11
#define vibeMotor 5
#define piezo 9
#define LED 13
long Start = 0;
// this section is Piezo Pitch
#define tonec     2500
#define toned     3900
#define tonee     3950
#define tonep       0

void setup() {
  // put your setup code here, to run once:
  pinMode(reedswitch, INPUT_PULLUP);
  pinMode(vibeMotor, OUTPUT);
  pinMode(piezo, OUTPUT);
  pinMode(LED, OUTPUT);
  digitalWrite(piezo, LOW);              INITIALIZE / DISABLE PIEZO 
  digitalWrite(vibeMotor, LOW);        INITIALIZE / STOP MOTOR 
 
 
}

void loop() {
  // put your main code here, to run repeatedly:
  begin_:
  if(!digitalRead(reedswitch)){//If reed switch active
    Start = millis();                            GET STARTUP TIME 
    //digitalWrite(LED2, HIGH); This would be for BALL in Hand LED
    while((millis()-Start)<6000){         IS RUNNING TIME < 6  SECONDS     
      if(digitalRead(reedswitch)){        RUNNING TIME < 6 SECONDS , CHECK THE SWITCH 
        goto begin_;                            SWITCH IS OFF, START OVER 
        break;                                     huh? HOW DO YOU  GET HERE ? 
      }
    }                                                 
   
    digitalWrite(vibeMotor, HIGH);
    Start = millis();
    while((millis()-Start)<50){
      if(digitalRead(reedswitch)){
        goto begin_;
        break;
      }
    }
    digitalWrite(LED, HIGH);
    beep(piezo,tonec,500);
    Start = millis();
    while((millis()-Start)<2000){
      if(digitalRead(reedswitch)){
        goto begin_;
        break;
      }
    }
    beep(piezo,toned,500);
    Start = millis();
    while((millis()-Start)<1000){
      if(digitalRead(reedswitch)){
        goto begin_;
        break;
      }
    }
    beep(piezo,tonee,500);
    Start = millis();
    while((millis()-Start)<1000){
      if(digitalRead(reedswitch)){
        goto begin_;
        break;
      }
    }

    beep(piezo,tonee,3000);
    Start = millis();
    while((millis()-Start)<1000){
      if(digitalRead(reedswitch)){
        goto begin_;
        break;
      }
    }
    //digitalWrite(vibeMotor, LOW);//turn off ibe motor, if you don't need this just comment out
  }
  digitalWrite(vibeMotor, LOW);
  digitalWrite(piezo, LOW);
  digitalWrite(LED, LOW);
}

void beep (unsigned char speakerPin, int frequencyInHertz, long timeInMilliseconds)
{
int x;
long delayAmount = (long)(1000000/frequencyInHertz);
long loopTime = (long)((timeInMilliseconds*1000)/(delayAmount*2));
for (x=0;x<loopTime;x++)
{
digitalWrite(speakerPin,HIGH);
delayMicroseconds(delayAmount);
digitalWrite(speakerPin,LOW);
delayMicroseconds(delayAmount);
}
}

Moderator edit: CODE TAGS ADDED