We usually use QQ in China. There are signs showing status( online, offline, busy, don't disturb) just like Skype. I think Skype and QQ are alike, but people here usually talk through sending messages instead of doing video chat.

People messaging you on Skype do know you are not online, but they are expecting you to respond as soon as you see their messages. Imagine you text somebody through cellphone, expect to get response, but there is none as time goes on. If you don't like the situation, just explain to them you have other things to do and can't check messages frequently, or tell them you don'k like they send messages on Skype when you are not online.

I think if you don't like you can tell them 

That's not your problem,and probably they are rookies.

Hi Ryan, just adding another thought...

I'm not sure what devices you are using for skype, but I know Skype will continue running as a background program on mobile devices (ie. if you don't log out properly) and make you seem online when you're not.

For example, if you log on to Skype on your phone then close the program, then log on through your laptop or PC then log out, you will still be shown as online thanks to your mobile. Has this possibility been considered?

Even then, I think a bit of netiquette is required from the people who went off at you for not answering. If you don't respond immediately, they should just leave it at that.