When I was a FI(R), I was told 'call me at home if you have a problem'.
This was never acceptable for a AFI but common place.
Prior to EASA the UK had Assistant Flying Instructors (AFI) and FI (Flying Instructors) so a clear distinction. The AFI being an assistant could not operate without a FI being present at the take-off and landing. The AFI was therefore always overseen - many consider this as being the true and only meaning of supervision. It could take a part time AFI two or more years to accrue sufficient experience to upgrade to FI. The AFI was required to be tested every 12 months and undertake a specific skill test to upgrade to a FI. To be a FI they were also required to be qualified to teach the IMC rating.
EASA dispensed with all of this. A FI is all that exists nowadays the (r) beside the title only means they cannot send first solos. They are not restricted in any other way and are not required to be overseen. They can even operate alone from a farmers field as long as they have an agreement with the farmer.