> The airlines stopped pumping exhaust into passenger compartments for a few years
This is way off the mark.
All airliners except for the Boeing 787 [0] pressurise the cabin with bleed air. This is not "exhaust"; it's pressurised air extracted upstream from the combustion stage. There are certain situations where the engine may ingest its own exhaust, or the exhaust of an aircraft in front, or there may be an internal leak in the bleed system. All of these are unintended contamination of the bleed air, not a normal mode of operation. In addition, the compressors ahead of the bleed valves must be lubricated and it is possible for this lubricant to get into the air stream if maintenance (including cleaning) is not carried out properly.
There was no period of time where airlines stopped pressurising the cabin with bleed air. It is the only source available on all airliners except the Boeing 787, and pressurisation is not optional.
[0] The Boeing 787 uses electric compressors to provide cabin air. This avoids some of the risks (leaks inside the engine, for example), but does nothing to avoid others (ingestion of exhaust from the same aircraft in certain wind conditions or from the aircraft in front when taxiing, or lubricants from the compressors getting into the air stream). The compressors are located in the wing-to-body fairing so the possibility to ingest external contaminants is quite similar to in traditional bleed air systems. The most noticeable difference on the Boeing 787 is the higher cabin pressure (lower cabin altitude) and higher humidity, both of which are made possible by structural improvements including the use of composites. Similar improvements (lower cabin altitude and higher humidity) are also present on e.g. the Airbus A350 and A380, which nonetheless — like all other airliners except the 787 — use traditional bleed air for pressurisation.