Most rentals have 3 “clocks”.
The regular clock on the panel that shows the time of day. But then there is a tachometer that measures total engine time (tach increases as the engine runs, but based on RPMs, not normal clock time). There is usually a Hobbs Meter in a rental that measures clock time while the engine is running.
Your lessons are likely charged by Hobbs.
Your dispatch, or log, or the CFI notes starting and ending Hobbs. The difference is what they charge you for the plane.
You could have 1.0 on the Hobbs, 0.7 on tach. Your logbook and the bill for the plane will reflect the 1.0.
The CFI time is usually billed separately from start to end of lesson (when you meet him in the office that clock usually starts ticking - some CFIs are generous and some watch every minute. Depends on personality and, likely, position in life. Young gun headed to the airlines needs every Penny. Retired airline capt sharing his passion has to charge something but he’s having fun.).
You’ll fly in winds up to 25 no problem, but I agree the first flight should have been on a smooth day. It’s no fun getting bounced around, even later in training, but definitely not day one with all new sounds, sights and sensations.
I remember my first flight. My dad paid the CFI without my knowledge while I was out looking at the planes for an open house. Ron, the CFI, came over and said “you can sit in there. Just scoot over to the left.” He sat/kneeled on the wing of the Cherokee 140 and explained all the gauges, controls etc. Then he said “let’s go for a short ride. I’ll promise you’ll love it.” My dad sort of shrugged from outside and said “I already paid. No refunds. Relax!”
Off we went. It was like a friendly ride. Smooth. Easy low bank turns. No abrupt movements/changes. I thought “God. This is amazing! Maybe I can do this too.” I was deathly afraid of heights and flying. That CFI and first flight was perfect . . . For me.
Definitely flew in rough uncomfortable air along the way but not the first few flights. Ron worked in the Steel Mills over near Gary and instructed on weekends now that his kids were away at college. That worked well for my personality.