Old house, traditional pine floorboards, 6mm ply, plus Ditra

[Time's Ran Out]

It sounds as though they have tried to do it correctly apart from the nails but only if the wooden section was deflection free.
The Ditra is an excellent product and used correctly, taped and adhered with the appropriate products will be fine.
They've taken the Ditra across the 2 substrates wood/concrete and used it as an anti crack membrane which may be ok, although the expansion joint should have been taken through to the tile surface! This can look unsightly but you should make sure to retain enough tiles to replace this area if it cracks in the future.
Without seeing the job it would be wrong to lamblast their work and other issues like heights etc may have been involved.

 

[Stef]

I'd using a decoupling membrane with trav on any floor...

I just saw it was travertine.
Yeah I would have used some form of decoupler..

 

[Stef]

I can't believe nails are being used and 6mm ply, your best bet is probably leave it and if at a later date it shows problems then contact the tiler.

They have probably used ring shank nails at that thickness of ply so it might hold.
Sounds like they have used af200 to fix the Ditra so that should stick well to the ply.
The Ditra is the saving grace here, if the ply doesn't debond then hopefully the tiles will be fine but only time will tell.