if you are exercising the privileges of a commercial certificate (which when your are instructing you by default have to be doing) then it is commercial flying.

and even if you don't log it (which is bad) there is someone else that will (the student, whose logbook you endorsed).

in general, if you fly for an airline, you give up the CFI gig. the only way to instruct and also fly a jet for someone and not have to worry about flight time limits is part 91.(Fractionals and corporate ops)