Do religious people - particularly belonging to religions of moral dogma - genuinely care about others well being?
Some do. Some don't. Though I would argue that everyone has at least few people who he cares about and that implies that they genuinely care about their well-being.
Or are they simply acting out of their own (Imagined) self interest (Scoring points for their afterlife game)?
What do you think about religious people who don't believe in an afterlife: why do they care about those things as the well being of others?(if they do,if they don't what do you think might be the real reason they believe in God?)
How can you know?
It's debatable if we can know anyone's true intentions (even our own) but IMO if there is something that can be a good indicator of the sincerity of someone's beliefs and the intentions behind them and that is doubt: that is leaving room for doubt and openness to discuss your beliefs.(this actually can be said about all people regardless of what they believe in, if they're religious or not) There is always a chance that our beliefs might be wrong and that by upholding those beliefs and acting in accordance with them we are hurting others instead of forming a loving relationship with others (which is something every religion preaches).
On the other hand absolute certainty in religious beliefs it's what can make even things like killing other people for your cause justifiable.
Also almost anyone who claims to know something with such certainty is probably trying to sell you something be it an idea or a specific thing.
How can they?
Not sure they can. Not sure any of us can. There is where belief kicks in. Nobody or most people don't believe they're bad or evil, their intentions seem truthful to them(do you think for example that suicide bombers have doubts about what they are doing might be wrong or perceive themselves as bad people:not likely, that's one example of a form that absolute conviction in something might result in). Again this is why I believe if anything can indicate sincerity in someone's belief that thing is having some doubt alongside with it.