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As a general rule, payment IDs are not necessary for transactions to go through, and if I'm not mistaken they will be deprecated in the next major version. Exchanges used to require them when receiving coins, so they know which user to credit with those coins. If you are sending the coins to a wallet you operate, you probably don't need a payment ID (unless you expect to receive the exact same amount from other sources too).
That being said, if the exchange's interface has a 'payment ID' field and they made it mandatory, there's nothing you can do about that.
If the exchange has indeed sent the coins, they could probably give you more information on the transaction, like in which block it was included. I would wait a bit and then contact their support.

Thank you very very much Chicken_76 for clearing that out. Unfortunately the payment ID was mandatory. So I am safe? With inputting anything there?

I am crazy concerned because this is the 2nd exchange that has some issues sending out to an external wallet, my first exchange is still transfering the coins for some unknown reason for several days now and support just got back to me with a response they are looking at it. The transaction failed and no coins was refunded. And now this. Sad

I always thought and had an impression transfers were automated.