Is my expectation wrong?
I'd say that the misperception here is that everyone has the same sense of urgency or an equal understanding of give and take. When you're up against a situation where you are going to give up something you care about to get work done, it's worth it to verify with both the boss and your coworkers what the urgency and tradeoffs are.
I often find with new employees and especially those who are new to the field at large, that the first urgent task is a matter of the utmost importance - there is no historical knowledge, so every issue looks huge. Over time, they learn that while most work is urgent not every task is a crisis, and it helps to check in and get a sense of urgency. Pacing yourself is important and the team coming to an agreement on the pace and urgency is also important.
What should I do?
I'd let this one go, but next time, plan ahead.
Things to try:
Urgent work - get a sense of what it means when an urgent and difficult task isn't finished on time. Managers love talking about the "critical path" - where anything on the path will cause further schedule delay if it slips a deadline. If your work isn't on this path, you may have far more slack to finish it, even if it is very important. This is a good discussion to have with the boss and any collaborators - everyone should get the same information on relative priorities and urgency.
Cross Time Zone Work - if you have to work with a collegue across time zones, it's worth while to figure out a pattern you can sustain, regardless of the urgency. Given that different people have different work/life demands, it's worth talking through a general plan before you have a real crisis. I often have the conversation of:
- On a regular basis I can... -- come in early and leave early, come in late, and stay late, meetup on weekends, etc. What's the least painful thing for you?
- In a crisis I can... -- what can you drop if you really had to push for something?
This is a case where you really do need to figure out what limits you are OK with. You're ticked off now, because you skipped stuff that was important to you, and your colleague didn't. It's quite possible that he didn't even know it was important work or that completing it was something you were sacrificing for. It's amazing how easily this communication can fall apart.
I am not sure if to let the manager know.
For a single case - no, skip it. For a trend that will cause problems if unaddressed - bring it up.
That's why it's really good to set up some shared expectations before you hit a crisis. If you and your colleague talk out how you can share work and what each of you can to when in a crunch, you can address this proactively. And it lets you hold your colleague to his promise - the email to the boss saying "we talked it out, and he's going to do XYZ, I'm going to do ABC" creates a contract. If later on, your colleague can't be found for XYZ, you're in a good position to say "hey, we told the boss we'd do this... what's up?"
Conversely, if you can't find a compromise, you can certainly say to the boss that you're worried. Generally in a crunch, 1 person doing a super-heroic level of effort while everyone else plods along will NOT be enough to save the project from difficulty. So if you find that that's the situation, you can raise your concern about manpower issues as a overall project risk, and not as "this guy is a slacker!!!".
Should I accept it as a fact?
Not necessarily. Every team, every office, and every industry is different. The norms for what constitute "enough" work will vary from place to place, be rewarded differently, and be seen in different ways politically.
Generally, a workplace can't survive and thrive without a core group of people who are willing to put in some extra effort in a crisis. The best workplaces are able to separate "crisis" from "every day business" so that they don't burn people out, and a thriving group will find a way to commonly communicate which state is true for today - crisis vs. day-to-day life.
And every individual is different. One person may be able to skip meals, another may simply require them, but be willing to work on the weekend. It's all about talking it out.
Getting into the groove with the team, and finding the right pace is a part of any job. But you may find that you like a more energetic pace than your current company offers. There are certainly big differences between jobs and very, very different corporate cultures on this score.