DVSA don’t care about WTD at the roadside, it’s only an issue when they’re doing an inspection of the operating centre. It really is down to the operator to keep the drivers right on WTD, or more accurately RTD.
As a driver, RTD applies and the only thing you could have opted out of was the night-time rules (10 hours work, but can still be on duty for 15)
Technically yes, you’re right to give it your attention, but from your own description it sounds like you’d be in breach of it anyways, so it’s a bit late now. 
I don’t see that it’s anything to be concerned about, but just be aware that your new employer might be one who needs to keep their drivers legal for RTD as well as EU/GB drivers hours; this was part of another thread over the past week.