Why would job center call me?

On all my claims so far I have never given my phone number out - as I prefer to get everything in writing, plus I have problems with answering the phone.

Wonder how that will effect the migration process for me.

It shouldn't make any difference whatsoever.

If you choose not to divulge your telephone number to the DWP as is my wont, that is your prerogative. Indeed, I would strongly advise claimants not to deal with any benefit-related matters with the DWP over the telephone, as there is a distinct possibility that vital evidence/information will go missing or will be misconstrued.