Unfortunately, how to manage a situation such as that depends very much on the people running the show. There's no single advisable course of action. At best, it's fair that you raise your concerns with your immediate manager and possibly HR.
You should also entertain the idea that you might not be reaching the expected output in your allotted hours but very cautiously as this is highly subjective. I've been in this boat before where I was expected to be as productive overnight as the developer that had been writing the codebase for over a year independently and knew it inside and out. We both had the same pay, expertise and ability but the other had a major advantage not adequately taken into consideration. The manager had given me times to complete things based on what he expected from his current employee. And these would be tight. I'm talking about things as low as hours, sometimes 15 minutes. I would have a list of tasks and the times for each like this, from the first week. I would often take 50% to three times longer just from figuring the system out and also trip over my shoe laces. If I did something in time it would be so rushed the quality were sacrificed and it would likely have bugs or issues later. Then a week or two after once I had actually learnt that system, I would be put on a new one with the idea that "maybe he'll do well on that instead". The expectations were impossible. After a few months we had a meeting and mutually agreed it would be best if we parted ways.
The worst thing is that I actually took the unreasonable targets seriously. This meant I was over taxing my mind to try to squeeze in both learning the system so to know it which my coworker already did and getting things done in a woefully insufficient amount of time to accommodate both. I couldn't sleep at night. I would toss and turn unable to sleep due to anxiety. Imagine finally being at home when after a day of having to work at an impossible pace when you should be in your comfort zone of having your mind to yourself it is filled with uncontrollable thoughts about what you need to get done next in the code. You end up feeling like you're in hell because of the stress. It was like being a slave. I started to withdraw, become very quiet and sucked into my own world. After leaving that I had burnt out and couldn't work for several months. Managers don't always get it right either so ensure to consider both sides of the coin. If I had more experience and confidence to confront my manager on these issues I think things would have turned out very differently. My work was well appreciated so not all was lost.
It isn't appropriate for people to establish their expectations in that manner unless its the type of role that explicitly depends on that. Depending where you are and how strongly you're being pressured into putting in additional hours for free that may end up being in violation of employment laws.
When I wanted to work for most than 48 hours a week I had to sign a letter of consent to voluntarily opt out from those protections. I often work late but I consider this a personal sacrifice. When managing I've never expected others to stay late because I do or work weekends. I also never present it as a standard that should be seen as normal. I am lucky to be in the position where I both do and manage people on what I do. So usually I take the hit and do the overtime. I only have others do it when absolutely necessary. In a management position, I don't believe that it's normal to ask employees to do overtime, that's a potential sign of failure on the company side. It's always an ask. Never an expectation. However, that means that when I do ask for it, people take it seriously.
I always abide by these guidelines...
- Going beyond the standard should not raise the standard:
The company should set a standard that people can get the work done adequately within the time contracted. It's only niche scenarios where anything but relatively infrequent overtime should be required. Any trained HR knows that excessive overtime might hide staffing issues, over commitment or inefficiency. Their primary job is ensuring that adequate human resources are provided so they need an accurate measure of that. Significant amounts of individual overtime as a personal sacrifice should largely be extra work, not necessary work.
Rare exceptions to this might be where the skillset is very hard to find and the overtime is of disproportionately high contribution towards a critical objective. Few people are genuinely likely to be in that position. It's a common managerial perception that this is the case when its often not. It's also a natural managerial desire to get the most out of the resources given and that can mean pushing people to work beyond their standard hours. In fact those resources aren't given to the manager, your contracted hours are, so he is extracting your personal resources.
- Measure the effect, not the cause:
When the company is not demanding overtime on its own terms, people should never directly be recompensed or evaluated base on their overtime. It's very easy to invent work or simply steal other people's in the name of making up overtime (work slower even or spend more time on the toilet). Instead results should be measured and for overtime work to contribute to that significantly the additional results from that have to be fairly decent.
In the absolute worst case your peer isn't even increasing output with overtime but instead compensating for their poor output. If merely their hours are being measure rather than output this will turn out very poorly for all involved.
To argue from the other side:
"The project schedule is tight".
In this case the normal thing is to commit if you can. The project is in trouble, it needs your help. Technically speaking you don't have to adhere to extremely unreasonable expectations but not putting a bit more in if the situation warrants it wont reflect well.
The problem with that is if every project has a tight schedule or the project schedule is tight for a long time or you don't think you doing overtime would help.
There are unwritten rules about this kind of thing where you might do unpaid overtime but it should come into play come next pay review or bonus time.
If you feel you can't trust your company to be honourable, that's another kettle of fish. Maybe it is, maybe it isn't, but if you don't take the risk you may never find yourself in an honourable company that rewards you for your efforts.
As others have mentioned, the solution to that might be to arrange some kind of official deferred recompense.
Your coworker may work the same way as I do. I work hard on faith with the hope of being rewarded eventually. That's my own personal risk to take however. That isn't the kind of risk you can often ask anyone to take other than entirely voluntarily. The only cases where that might be different are things like a start up or company with a shaky financial situation with a set budget and it's either make or bust. That is, if things don't work out they have no means to even pay you let alone reward you.