Hi again! Yes, the total time includes the warm-up.
The 15-20 mins is an estimate, but the time needed to really warm up will differ by person and by day. For instance, at 52 and slow-twitch dominant, some days it takes a good hour for my body to fully ‘come online’. During that time my body is still working – heart, lungs, muscle fibres, metabolism etc. – so that time needs to be included in the total time.