You've been training Mike, a new employee, via OJT. Mike is in his second week on the job. Formerly, you were partnered with an experienced person, and the two of you were an efficient team. There's a lot of ground to cover, and your boss (Janet) allowed for that during a discussion you had just before she left for two weeks of vacation near the end of Mike's first week on the job.
Your temporary boss, Phil, has a different attitude. Near the end of Mike's second week, Phil told you he expects the two of you to complete work “at the normal rate.” When you asked for a definition of “normal rate,” Phil told you to “quit fooling around with all the safety paranoia, especially those lengthy job briefings and all the time verbally rehearsing procedures before doing the work.”
When you tried to explain that Mike wasn't ready to proceed at full speed yet, Phil threatened to write you up for insubordination if you didn't “get your act together.” You replied that you'd worked out this plan with Janet, to which Phil replied by saying: “She's not here.
Phil does have the power to sully your employment record, if not get you fired, before Janet returns. Your cause is not helped by the fact that you lack written instructions from Janet regarding the OJT. What should you do?
You could ask Phil to assign someone else to mentor Mike. That would take you off the hook. But it would force a coworker to deal with the same issue, and this passing of the buck won't be appreciated.
You could agree with Phil to do what he says, then just don't do it. Probably, he won't notice since perhaps mentally he checked off the box and has other things on his plate, such as covering for Janet while she is gone. But that's dishonest.
Phil didn't say to stop the job briefings or to stop going over procedures before doing the work. He merely accused you of milking the job. What you have is a difference of opinion as to how much OJT this trainee needs.
One approach is to ask Phil if you can discuss this again. Start off by telling him you heard and understood what he said about the job briefings and you will gradually shorten those under the assumption Mike is learning and needs less instruction.
Then ask Phil if he can relax his standards until Janet is back. Then she can assess the situation since any productivity deficits for her crews would fall on her anyhow. This is reasonable, and you are asking for barely more than a week. Phil should go for it, but if he does not then you must take a different approach.
Because Phil said he expects the rate of work to be “normal” he is dismissing the fact that Mike is a trainee and a new employee. That means Phil is probably violating company policy. If the relevant company policy documents support this as fact, great. Otherwise, you will have to turn to the OSHA regulations and definition of “qualified person.” Meet with your HR rep to discuss this issue and your solution that Phil turned down.
If the HR rep won't help, go to Phil's boss (who is also Janet's boss). Their boss won't want to mess with this, and will probably just tell Phil to back off until Janet gets back in barely more than a week.
Always keep in mind that thorough training is worth the investment, especially when it comes to safety. If you “save time” by taking shortcuts with Mike's training and something tragic happens, Mike will not get a “do over.”