When someone's name appears on a memorial, there's no guarantee that they are buried there - my wife has found one in Kent which names family members who had emigrated to the USA and died there, and I'm sure she's not the only one.
In this case, the inscription suggests to me that the stone was placed there after Ada died, and her surviving children decided to commemorate Herbert Alfred and Annie as well - and they could have been buried anywhere. There's also the possibility that Herbert Alfred and/or Annie were buried there first, and then Ada, but that the stone wasn't placed there until she died. The only way of knowing for certain who is buried there would be to check the cemetery burial records.
The birth of a Herbert Alfred Hayes was registered in Middlesbrough in Dec qtr 1903 (9d 591), which seems possible. I'll leave looking for Annie to you...

Arthur