How is the fuel quality monitored/assured for jetliners?
As you can see, the supply chain is big (with filters and water separators at various points). The short answer is that standards and quality checks are followed.

As for the jetliners, as far as I know they can't detect the fuel quality, but some can alert if issues arise in the fuel filters. The certification standards focus on engine restart capability and that it...


  ... should be demonstrated for the momentary shutdown from a high power or thrust setting, associated with the takeoff and climb flight regimes, and the extended shutdown at medium to high altitude where the engines may be "windmilling" and/or "cold soaked."


Fuel contamination is of the reasons mentioned in the engine restart section.



ICAO's Manual on Civil Aviation Jet Fuel Supply (on SKYbrary; PDF) is comprehensive as to the practices involved (the image above is from the manual).


  1.2.1 Any business entity involved in the aviation fuel supply chain has an obligation to implement and comply with industry and/or company proprietary PSPs, as described in this manual, that cover the activities in which they are involved.


Supply and distribution, aircraft operators, and airport operators, each follow their respective policies, standards and procedures (PSP).


  3.10.1 Any organization that manufactures, supplies or handles aviation fuel should have a documented training programme for its personnel. The programme should cover product quality, safe operation of equipment, emergency procedures and occupational health, as well as management systems for operational safety, environment and security. In particular, the programme should include in its scope a systematic way to identify hazards and effectively control risks to fuel quality, personnel, and facility and equipment or aircraft safety.


At each step the manual lists the various industry standards and manuals to follow.