Like I stated earlier, a business in which crisis are so frequent as to occur daily or weekly, is badly mismanaged and dysfunctional. Such companies will hide under false pretenses like "that's just the way the industry works", while frankly straight up abusing developers. Crisis should by all means be extremely infrequent, otherwise there's a major management problem, which of course can't be the developers responsibility. I'll restate from all my replies in this thread, that if OP is in such a company, he should leave.
2) In the variety of European countries where I've worked, compensation for over-time is a non-issue - I did not mention compensation explicitly, as it's obvious to me - it's indeed against the law not to compensate. You'd either get full-pay, 50% to 100% increase (usually for night and weekend work), or you'd get time off. From yours and other responses, I gather this is not the standard in the US.
3) Certainly there were deployment procedures, however this developer decided to bypass staging, testing and even didn't perform a smoke test which would have shown the crashed application. He deemed his code of such high quality that nothing could possibly go wrong. And while he didn't follow procedure and therefore caused a minor scandal for this particular company's public image and lots of lost customers, he didn't see why he should be involved in recovery, since it was after 5 o clock. Instead his teammates worked until long into the night, to find out what had actually happened before finally fixing it.
1) The fire in the kitchen isn't the developer's responsibility as he is an employee and does not own the property or the problem. The company is hiring the developer to do work for them - that work includes fixing problems regardless of who created them. If the developer were on a contract for 1 month and something he created exploded on 1month+1day then the developer is under no responsibility to fix that problem. That extends just the same to an employee and shows how the employee is not responsible for the fire. Of course, most employees are going to happily stay and fix what they broke as it's part of professional integrity - but the business owner should really be saying "thank you" in that situation as the employee has gone beyond his employment contract to help. So I disagree with you - the developer being the only one able to solve a problem does not make him responsible in any way. If the developer received the rewards of ownership then he would be responsible.
I'll admit that it doesn't work like this in most cases as employees are scared of getting fired and act more like indentured servants than anything - but as a manager you should try to be above that, I think.
2) Definitely not standard - and the OP who you wrote your comment to is clearly not being offered overtime. He is being told to work more with no mention of more pay. The company wouldn't want him working overtime if it was costing them more than hiring another employee.
3) So the developer deliberately sabotaged established company procedure. I'm not sure what it has to do with the OP so it's probably why the replies to your comment seem confused. At any rate, it's a completely separate issue and even if the dev stayed all weekend to fix the problem, he should still be getting a very stern official warning to follow safety procedures. Seems like an orthogonal issue.
I also noticed you didn't write anything about compensation and that's why I did. That developer that insisted on leaving at 5 because that's what his job was? I can assure you that if you paid him a multiple of his standard rate and made it clear that he was doing the business a favor then he would remain there to help fix the fire.
Also regarding deploying breaking changes five minutes before leaving - I'm assuming this means it was standard procedure to deploy non-breaking changes five minutes before leaving as well. This feels like a management problem. Those changes should be deployed to a staging environment of some kind and not directly to production without some kind of testing or sign off procedure as then it doesn't matter if they break anything as it will continue to be worked on the following day without affecting customers.