I have never got my tickets checked on my SWR / Southern / CrossCountry journeys so far, including numerous journeys between Bournemouth and Poole, and round trip Bournemouth - Southampton - Brighton on the coastal line. However, my journey yesterday on GWR had my tickets checked just north of Salisbury on both bounds.
I have made a few more train journeys in the last week and got my ticket checked a few times.
Summary for this year since May:
CrossCountry Bournemouth - Southampton Central: not checked
Great Western Railway between Salisbury and Bristol Temple Meads: both bound north of Salisbury
South Western Railway between Bournemouth and Branksome / Poole: none at all for 11 trips
South Western Railway between Bournemouth and Southampton: 3 out of 5 trips
- eastbound on London-bound stopping at Brockenhurst only: checked before and after Brockenhurst
- eastbound on Winchester-bound stopping service: checked after Brockenhurst
- westbound on Weymouth-bound non-stop service: checked
- westbound on Weymouth-bound service stopping at Brockenhust only: not checked
- westbound on Poole-bound stopping service: not checked
Southern between Southampton and Brighton: not checked